Thalmaier, Anton
Overview
Works:  22 works in 56 publications in 3 languages and 1,168 library holdings 

Roles:  Author, Other, Thesis advisor, htt, Opponent 
Classifications:  HG106, 332.01519232 
Publication Timeline
.
Most widely held works by
Anton Thalmaier
Stochastic calculus of variations in mathematical finance by
Paul Malliavin(
)
25 editions published between 2004 and 2010 in English and held by 980 WorldCat member libraries worldwide
This new book, demonstrating the relevance of Malliavin calculus for Mathematical Finance, starts with an exposition from scratch of this theory. The last chapter gives an introduction to the same objects in the context of jump processes where incomplete markets appear
25 editions published between 2004 and 2010 in English and held by 980 WorldCat member libraries worldwide
This new book, demonstrating the relevance of Malliavin calculus for Mathematical Finance, starts with an exposition from scratch of this theory. The last chapter gives an introduction to the same objects in the context of jump processes where incomplete markets appear
Stochastische Analysis : eine Einführung in die Theorie der stetigen Semimartingale by
W Hackenbroch(
Book
)
4 editions published in 1994 in German and held by 106 WorldCat member libraries worldwide
" ... Dieses Buch gibt einen guten Überblick über die mathematische Theorie der stochastischen Semimartingale, kann selbstverstñdlich nicht alle Gebiete vollstñdig abdecken, behandelt jedoch die Kernpunkte hervorragend." C. Cenker. Monatshefte für Mathematik, Wien " ... Zusammenfassend ist dieses Buch sicher als ein Standardwerk der stochastischen Analysis anzusehen und kann vorbehaltlos empfohlen werden." G. Eder. Internationale Mathematische Nachrichten, Wien "In summary, it can be stated that the authors deserve acknowledgemnt for their courage in undertaking an immense work in collecting material, arranging it consistently and writing it up in a neat fashion. Moreover, they succeeded in stressing the wellknown message that entering stochastic analysis with the aim of reaching a deeper understanding of the theory and its methods can hardly be achieved 'without tears'. One admires the authors even more once one realizes that they both are selftaught in the field they are writing about and that the second named author just started to publish on the subject." H. Heyer. Metrika
4 editions published in 1994 in German and held by 106 WorldCat member libraries worldwide
" ... Dieses Buch gibt einen guten Überblick über die mathematische Theorie der stochastischen Semimartingale, kann selbstverstñdlich nicht alle Gebiete vollstñdig abdecken, behandelt jedoch die Kernpunkte hervorragend." C. Cenker. Monatshefte für Mathematik, Wien " ... Zusammenfassend ist dieses Buch sicher als ein Standardwerk der stochastischen Analysis anzusehen und kann vorbehaltlos empfohlen werden." G. Eder. Internationale Mathematische Nachrichten, Wien "In summary, it can be stated that the authors deserve acknowledgemnt for their courage in undertaking an immense work in collecting material, arranging it consistently and writing it up in a neat fashion. Moreover, they succeeded in stressing the wellknown message that entering stochastic analysis with the aim of reaching a deeper understanding of the theory and its methods can hardly be achieved 'without tears'. One admires the authors even more once one realizes that they both are selftaught in the field they are writing about and that the second named author just started to publish on the subject." H. Heyer. Metrika
Asymptotik Brownscher Bewegungen im Zusammenhang mit geometrischen und potentialtheoretischen Eigenschaften Riemannscher Mannigfaltigkeiten
negativer Krümmung by
Anton Thalmaier(
Book
)
5 editions published in 1989 in German and held by 31 WorldCat member libraries worldwide
5 editions published in 1989 in German and held by 31 WorldCat member libraries worldwide
Stochastic calculus of variations in financial mathematics by
Paul Malliavin(
Book
)
2 editions published in 2004 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 9 WorldCat member libraries worldwide
Stochastic calculus of variations in financial mathematics by
Paul Malliavin(
Book
)
1 edition published in 2006 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 8 WorldCat member libraries worldwide
Heat equation derivative formulas for vector bundles by Bruce K Driver(
Book
)
2 editions published in 2000 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 2000 in English and held by 6 WorldCat member libraries worldwide
Arbeitsgemeinschaft GeyerHarder über Brownsche Bewegung auf Riemannsche Mannigfaltigkeiten : 2.10. bis 8.10.1988(
Book
)
2 editions published in 1988 in German and held by 4 WorldCat member libraries worldwide
A.H. Assadi, Bonn; B. Brinkmatili, Bochum; W. Ballmann, Zürich; Th. Bröcker, Regensburg; W. Bauer, Regensburg; H. Crauel, Bremen; C. Beckmatiti, Köln; C. Deninger, Regensburg; K. Bichteler, Austin; E. Eberlein, Freiburg; W.D Geyer, Erlangen; N. Jacob, Erlangen; W. Hackerbroch, Regensburg; K. Jänich, Regensburg; G. Harder, Bonn; U. Jannsen, Regensburg; A. Hilbert, Bochum; K. Kaie, Augsburg; W. Hoh, Nürnberg; H. Kareher, Bonn; N. Klingen, Köln; R. Leandre, Straßburg; B. Köck, Regensburg; B. Leeb, Bonn; P. Kröger, Erlangen; L. Miller, Karlsruhe; H. Kurke, Berlin; B. Moonetl, Bonn; A. Langer, Köln; S. MüllerStach, Bayreuth; J. Neukirch, Regensburg; M. Roller, Regensburg; S.J.A. Paycha, Bochum; M. Rost, Regensburg; R. Pink, Bonn; M. Schlichenmaier, Mannheim; M. Puschnigg, Bonn; P. Schneider, Köln; M. Rapoport, Bonn; W.K. Seiler, Mannheim; P. Singer, Erlangen; A. Vogt, Regensburg; W. Stich, Köfering; M. Weiand, Köln; U. Stuher, Wuppertal; R. Weissauer, Mannheim; T. Sturm, Erlangen; K. Wingberg, Erlangen; A. Thalmaier, Regensburg
2 editions published in 1988 in German and held by 4 WorldCat member libraries worldwide
A.H. Assadi, Bonn; B. Brinkmatili, Bochum; W. Ballmann, Zürich; Th. Bröcker, Regensburg; W. Bauer, Regensburg; H. Crauel, Bremen; C. Beckmatiti, Köln; C. Deninger, Regensburg; K. Bichteler, Austin; E. Eberlein, Freiburg; W.D Geyer, Erlangen; N. Jacob, Erlangen; W. Hackerbroch, Regensburg; K. Jänich, Regensburg; G. Harder, Bonn; U. Jannsen, Regensburg; A. Hilbert, Bochum; K. Kaie, Augsburg; W. Hoh, Nürnberg; H. Kareher, Bonn; N. Klingen, Köln; R. Leandre, Straßburg; B. Köck, Regensburg; B. Leeb, Bonn; P. Kröger, Erlangen; L. Miller, Karlsruhe; H. Kurke, Berlin; B. Moonetl, Bonn; A. Langer, Köln; S. MüllerStach, Bayreuth; J. Neukirch, Regensburg; M. Roller, Regensburg; S.J.A. Paycha, Bochum; M. Rost, Regensburg; R. Pink, Bonn; M. Schlichenmaier, Mannheim; M. Puschnigg, Bonn; P. Schneider, Köln; M. Rapoport, Bonn; W.K. Seiler, Mannheim; P. Singer, Erlangen; A. Vogt, Regensburg; W. Stich, Köfering; M. Weiand, Köln; U. Stuher, Wuppertal; R. Weissauer, Mannheim; T. Sturm, Erlangen; K. Wingberg, Erlangen; A. Thalmaier, Regensburg
Heat equation derivative formulas for vector bundles by Bruce K Driver(
Book
)
1 edition published in 2000 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2000 in English and held by 4 WorldCat member libraries worldwide
Etude d'équations d'évolution en géométrie globale avec des méthodes probabilistes by
Abdoulaye Koléhè CoulibalyPasquier(
Book
)
1 edition published in 2009 in French and held by 2 WorldCat member libraries worldwide
In the first part of this thesis, for a family of metrics on a manifold we associate a Brownian motion. We build a parallel stochastic transport above this process. With a kind of intrinsic stochastic flow, we define a notion of damped parallel transport above this process. We characterize the Ricci flow as the only flow of metrics that guarantees the equality between the parallel transport and the damped parallel transport. We deduce some properties of the Ricci flow. On the second hand, we study the mean curvature flow of a hypersurface. We build a process without birth and we prove the uniqueness in law of such a process when the initial hypersurface is strictly convex. When it is not strictly convex we obtain a family of martingales that start in a singular “manifold”. In the last part, we build a diffusion in the space of regular curves on some manifold. We deduce sufficient conditions to obtain some contraction properties  for a large class of Wasserstein distances  between two measures of probability that represent the density of two diffusions associated with an inhomogeneous elliptic operator. So this new construction yields a totally probabilistic alternative to the Otto calculus used by Lott to obtain similar results
1 edition published in 2009 in French and held by 2 WorldCat member libraries worldwide
In the first part of this thesis, for a family of metrics on a manifold we associate a Brownian motion. We build a parallel stochastic transport above this process. With a kind of intrinsic stochastic flow, we define a notion of damped parallel transport above this process. We characterize the Ricci flow as the only flow of metrics that guarantees the equality between the parallel transport and the damped parallel transport. We deduce some properties of the Ricci flow. On the second hand, we study the mean curvature flow of a hypersurface. We build a process without birth and we prove the uniqueness in law of such a process when the initial hypersurface is strictly convex. When it is not strictly convex we obtain a family of martingales that start in a singular “manifold”. In the last part, we build a diffusion in the space of regular curves on some manifold. We deduce sufficient conditions to obtain some contraction properties  for a large class of Wasserstein distances  between two measures of probability that represent the density of two diffusions associated with an inhomogeneous elliptic operator. So this new construction yields a totally probabilistic alternative to the Otto calculus used by Lott to obtain similar results
SubLaplacian comparison theorems on totally geodesic Riemannian foliations by
Fabrice Baudoin(
)
1 edition published in 2019 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2019 in English and held by 2 WorldCat member libraries worldwide
Characterization of Pinched Ricci Curvature by Functional Inequalities by LiJuan Cheng(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Functional inequalities on manifolds with nonconvex boundary by
Lijuan Cheng(
)
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
Stochastic Completeness and Gradient Representations for SubRiemannian Manifolds by
Erlend Grong(
)
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
Uniform gradient estimates on manifolds with a boundary and applications by LiJuan Cheng(
)
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
Etude d'équations d'évolution en géométrie globale avec des méthodes probabilistes by
Abdoulaye Koléhè CoulibalyPasquier(
)
1 edition published in 2009 in French and held by 1 WorldCat member library worldwide
Dans la première partie de cette thèse, à une famille de métriques sur une variété nous associons un mouvement brownien. Nous construisons un transport parallèle stochastique audessus de ce processus. Avec une forme intrinsèque du flot stochastique, nous définissons une notion de transport parallèle déformé audessus de ce processus. Nous caractérisons le flot de Ricci comme étant le seul flot sur les métriques garantissant l'égalité du tranport parallèle et du transport parallèle déformé. Dans ce cas, le transport parallèle déformé est une isométrie. Nous en déduisons des propriétés sur le flot de Ricci. Dans une seconde partie, nous nous intéressons au flot à courbure moyenne d'une hypersurface. Nous construisons ainsi un processus sans naissance et nous montrons son unicité en loi quand la variété de départ est strictement convexe. Quand l'hypersurface de départ n'est pas strictement convexe nous avons néanmoins une famille de martingales dont les points de départ sont sur une "variété" singulière. Dans la dernière partie, nous construisons une diffusion dans l'espace des courbes sur une variété. Nous en déduisons des conditions suffisantes pour obtenir des propriétés de contraction  pour plusieurs distances de Wasserstein  entre deux mesures de probabilité représentant la densité de deux diffusions d'opérateur elliptique inhomogène quelconque. Ainsi, cette nouvelle construction produit une alternative entièrement probabiliste aux calculs d'Otto utilisés par Lott pour arriver à des résultats similaires
1 edition published in 2009 in French and held by 1 WorldCat member library worldwide
Dans la première partie de cette thèse, à une famille de métriques sur une variété nous associons un mouvement brownien. Nous construisons un transport parallèle stochastique audessus de ce processus. Avec une forme intrinsèque du flot stochastique, nous définissons une notion de transport parallèle déformé audessus de ce processus. Nous caractérisons le flot de Ricci comme étant le seul flot sur les métriques garantissant l'égalité du tranport parallèle et du transport parallèle déformé. Dans ce cas, le transport parallèle déformé est une isométrie. Nous en déduisons des propriétés sur le flot de Ricci. Dans une seconde partie, nous nous intéressons au flot à courbure moyenne d'une hypersurface. Nous construisons ainsi un processus sans naissance et nous montrons son unicité en loi quand la variété de départ est strictement convexe. Quand l'hypersurface de départ n'est pas strictement convexe nous avons néanmoins une famille de martingales dont les points de départ sont sur une "variété" singulière. Dans la dernière partie, nous construisons une diffusion dans l'espace des courbes sur une variété. Nous en déduisons des conditions suffisantes pour obtenir des propriétés de contraction  pour plusieurs distances de Wasserstein  entre deux mesures de probabilité représentant la densité de deux diffusions d'opérateur elliptique inhomogène quelconque. Ainsi, cette nouvelle construction produit une alternative entièrement probabiliste aux calculs d'Otto utilisés par Lott pour arriver à des résultats similaires
Modélisation financière avec des processus de Volterra et applications aux options, aux taux d'intérêt et aux risques
de crédit by
Sami El Rahouli(
)
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
This work investigates financial models for option pricing, interest rates and credit risk with stochastic processes that have memory and discontinuities. These models are formulated in terms of the fractional Brownian motion, the fractional or filtered Lévy process (also doubly stochastic) and their approximations by semimartingales. Their stochastic calculus is treated in the sense of Malliavin and Itô formulas are derived. We characterize the riskneutral probability measures in terms of these processes for options pricing models of BlackScholes type with jumps. We also study models of interest rates, in particular the models of Vasicek, CoxIngersollRoss and HeathJarrowMorton. Finally we study credit risk models
1 edition published in 2014 in English and held by 1 WorldCat member library worldwide
This work investigates financial models for option pricing, interest rates and credit risk with stochastic processes that have memory and discontinuities. These models are formulated in terms of the fractional Brownian motion, the fractional or filtered Lévy process (also doubly stochastic) and their approximations by semimartingales. Their stochastic calculus is treated in the sense of Malliavin and Itô formulas are derived. We characterize the riskneutral probability measures in terms of these processes for options pricing models of BlackScholes type with jumps. We also study models of interest rates, in particular the models of Vasicek, CoxIngersollRoss and HeathJarrowMorton. Finally we study credit risk models
The C*algebras of certain Lie groups by
JanneKathrin Günther(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
In this doctoral thesis, the C*algebras of the connected real twostep nilpotent Lie groups and the Lie group SL(2,R) are characterized. Furthermore, as a preparation for an analysis of its C*algebra, the topology of the spectrum of the semidirect product U(n) x H_n is described, where H_n denotes the Heisenberg Lie group and U(n) the unitary group acting by automorphisms on H_n. For the determination of the group C*algebras, the operator valued Fourier transform is used in order to map the respective C*algebra into the algebra of all bounded operator fields over its spectrum. One has to find the conditions that are satisfied by the image of this C*algebra under the Fourier transform and the aim is to characterize it through these conditions. In the present thesis, it is proved that both the C*algebras of the connected real twostep nilpotent Lie groups and the C*algebra of SL(2,R) fulfill the same conditions, namely the “norm controlled dual limit” conditions. Thereby, these C*algebras are described in this work and the “norm controlled dual limit” conditions are explicitly computed in both cases. The methods used for the twostep nilpotent Lie groups and the group SL(2,R) are completely different from each other. For the twostep nilpotent Lie groups, one regards their coadjoint orbits and uses the Kirillov theory, while for the group SL(2,R) one can accomplish the calculations more directly
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
In this doctoral thesis, the C*algebras of the connected real twostep nilpotent Lie groups and the Lie group SL(2,R) are characterized. Furthermore, as a preparation for an analysis of its C*algebra, the topology of the spectrum of the semidirect product U(n) x H_n is described, where H_n denotes the Heisenberg Lie group and U(n) the unitary group acting by automorphisms on H_n. For the determination of the group C*algebras, the operator valued Fourier transform is used in order to map the respective C*algebra into the algebra of all bounded operator fields over its spectrum. One has to find the conditions that are satisfied by the image of this C*algebra under the Fourier transform and the aim is to characterize it through these conditions. In the present thesis, it is proved that both the C*algebras of the connected real twostep nilpotent Lie groups and the C*algebra of SL(2,R) fulfill the same conditions, namely the “norm controlled dual limit” conditions. Thereby, these C*algebras are described in this work and the “norm controlled dual limit” conditions are explicitly computed in both cases. The methods used for the twostep nilpotent Lie groups and the group SL(2,R) are completely different from each other. For the twostep nilpotent Lie groups, one regards their coadjoint orbits and uses the Kirillov theory, while for the group SL(2,R) one can accomplish the calculations more directly
The pricevolatility feedback rate: an implementable mathematical indicator of market stability(
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Courbure de Ricci grossière de processus markoviens by
Laurent Veysseire(
)
1 edition published in 2012 in French and held by 1 WorldCat member library worldwide
The coarse Ricci curvature of a Markov process on a Polish space is defined as a local contraction rate of the W1 Wasserstein distance between the laws of the process starting at two different points. The first part of this thesis deals with results holding in the case of general Polish spaces. The simplest of them is that the infimum of the coarse Ricci curvature is a global contraction rate of the semigroup of the process for the W1 distance between probability measures. Though intuitive, this result is diffucult to prove in continuous time. The proof of this result, and the following consequences for the spectral gap of the generator are the subject of Chapter 1. Another interesting result, using the values of the coarse Ricci curvature at different points, and not only its infimum, is a concentration result for the equilibrium measures, only holding in a discrete time framework. That will be the topic of Chapter 2. The second part of this thesis deals with the particular case of diffusions on Riemannian manifolds. A formula is given, allowing to get the coarse Ricci curvature from the generator of the diffusion. In the case when the metric is adapted to the diffusion, we show the existence of a coupling between the paths starting at two different points, such that the coarse Ricci curvature is exactly the decreasing rate of the distance between these paths. We can then show that the spectral gap of the generator is at least the harmonic mean of the Ricci curvature. This result can be generalized when the metric is not the one induced by the generator, but it needs a very restricting hypothesis, and the curvature we have to choose is smaller
1 edition published in 2012 in French and held by 1 WorldCat member library worldwide
The coarse Ricci curvature of a Markov process on a Polish space is defined as a local contraction rate of the W1 Wasserstein distance between the laws of the process starting at two different points. The first part of this thesis deals with results holding in the case of general Polish spaces. The simplest of them is that the infimum of the coarse Ricci curvature is a global contraction rate of the semigroup of the process for the W1 distance between probability measures. Though intuitive, this result is diffucult to prove in continuous time. The proof of this result, and the following consequences for the spectral gap of the generator are the subject of Chapter 1. Another interesting result, using the values of the coarse Ricci curvature at different points, and not only its infimum, is a concentration result for the equilibrium measures, only holding in a discrete time framework. That will be the topic of Chapter 2. The second part of this thesis deals with the particular case of diffusions on Riemannian manifolds. A formula is given, allowing to get the coarse Ricci curvature from the generator of the diffusion. In the case when the metric is adapted to the diffusion, we show the existence of a coupling between the paths starting at two different points, such that the coarse Ricci curvature is exactly the decreasing rate of the distance between these paths. We can then show that the spectral gap of the generator is at least the harmonic mean of the Ricci curvature. This result can be generalized when the metric is not the one induced by the generator, but it needs a very restricting hypothesis, and the curvature we have to choose is smaller
Beiträge zur Geometrie von Brownschen Bewegungen und Martingalen auf Riemannschen Mannigfaltigkeiten by
Anton Thalmaier(
Book
)
1 edition published in 1998 in German and held by 1 WorldCat member library worldwide
1 edition published in 1998 in German and held by 1 WorldCat member library worldwide
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Related Identities
 Malliavin, Paul 19252010 Author
 Hackenbroch, W. (Wolfgang) Author
 SpringerLink (Online service) Other
 Driver, Bruce K. Author
 Deninger, Christopher 1958 Editor
 Thompson, James Other
 Grong, Erlend Author
 Cheng, LiJuan Author
 Université de Poitiers Degree grantor
 CoulibalyPasquier, Abdoulaye Koléhè (1981....). Author