skip to content
Semiclassical analysis for diffusions and stochastic processes Preview this item
ClosePreview this item
Checking...

Semiclassical analysis for diffusions and stochastic processes

Author: V N Kolokolʹt︠s︡ov
Publisher: Berlin ; New York : Springer, ©2000.
Series: Lecture notes in mathematics (Springer-Verlag), 1724.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes.  Read more...

Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Additional Physical Format: Online version:
Kolokolʹt︠s︡ov, V.N. (Vasiliĭ Nikitich).
Semiclassical analysis for diffusions and stochastic processes.
Berlin ; New York : Springer, ©2000
(OCoLC)654536378
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: V N Kolokolʹt︠s︡ov
ISBN: 3540669728 9783540669722 013028128X 9780130281289
OCLC Number: 43555169
Description: viii, 345 pages : illustrations ; 24 cm.
Contents: Ch. 1. Gaussian diffusions. 1. Gaussian diffusion. Probabilistic and analytic approaches. 2. Classification of Gaussian diffusions by the Young schemes. 3. Long time behaviour of the Green functions of Gaussian diffusions. 4. Complex stochastic Gaussian diffusion. 5. The rate of escape for Gaussian diffusions and scattering for its perturbations --
Ch. 2. Boundary value problem for Hamiltonian systems. 1. Rapid course in calculus of variations. 2. Boundary value problem for non-degenerate Hamiltonians. 3. Regular degenerate Hamiltonians of the first rank. 4. General regular Hamiltonians depending quadratically on momenta. 5. Hamiltonians of exponential growth in momenta. 6. Complex Hamiltonians and calculus of variations of saddle-points. 7. Stochastic Hamiltonians --
Ch. 3. Semiclassical approximation for regular diffusion. 1. Main ideas of the WKB-method with imaginary phase. 2. Calculation of the two-point function for regular Hamiltonians. 3. Asymptotic solutions of the transport equation. 4. Local asymptotics of the Green function for regular Hamiltonians. 5. Global small diffusion asymptotics and large deviations. 6. Asymptotics for non-regular diffusion: an example. 7. Analytic solutions to some linear PDE --
Ch. 4. Invariant degenerate diffusion on cotangent bundles. 1. Curvilinear Ornstein-Uhlenbeck process and stochastic geodesic flow. 2. Small time asymptotics for stochastic geodesic flow. 3. The trace of the Green function and geometric invariants --
Ch. 5. Transition probability densities for stable jump-diffusion. 1. Asymptotic properties of one-dimensional stable laws. 2. Asymptotic properties of finite-dimensional stable laws. 3. Transition probability densities for stable jump-diffusion. 4. Stable jump-diffusions combined with compound Poisson processes. 5. Stable-like processes. 6. Applications to the sample path properties of stable jump-diffusions. Ch. 6. Semiclassical asymptotics for the localised Feller-Courrege processes. 1. Maslov's tunnel equations and the Feller-Courrege processes. 2. Rough local asymptotics and local large deviations. 3. Refinement and globalisation --
Ch. 7. Complex stochastic diffusions or stochastic Schrodinger equations. 1. Semiclassical approximation: formal asymptotics. 2. Semiclassical approximation: justification and globalisation. 3. Applications: two-sided estimates to complex heat kernels, large deviation principle, well-posedness of the Cauchy problem. 4. Path integration and infinite-dimensional saddle-point method --
Ch. 8. Some topics in semiclassical spectral analysis. 1. Double-well splitting. 2. Low lying eigenvalues of diffusion operators and the life-times of diffusion processes. 3. Quasi-modes of diffusion operators around a closed orbit of the corresponding classical system --
Ch. 9. Path integration for the Schrodinger, heat and complex stochastic diffusion equations. 1. Introduction. 2. Path integral for the Schrodinger equation in p-representation. 3. Path integral for the Schrodinger equation in x-representation. 4. Singular potentials. 5. Semiclassical asymptotics. 6. Fock space representation --
App. A. Main equation of the theory of continuous quantum measurements --
App. B. Asymptotics of Laplace integrals with complex phase --
App. C. Characteristic functions of stable laws --
App. D. Levy-Khintchine [Psi]DO and Feller-Courrege processes --
App. E. Equivalence of convex functions --
App. F. Unimodality of symmetric stable laws --
App. G. Infinite divisible complex distributions and complex Markov processes --
App. H.A review of main approaches to the rigorous construction of path integral --
App. I. Perspectives and problems.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1724.
Responsibility: Vassili N. Kolokoltsov.
More information:

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/43555169> # Semiclassical analysis for diffusions and stochastic processes
    a schema:Book, schema:CreativeWork ;
   library:oclcnum "43555169" ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/42837#Place/berlin> ; # Berlin
   library:placeOfPublication <http://dbpedia.org/resource/New_York_City> ; # New York
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/gw> ;
   schema:about <http://dewey.info/class/510/e21/> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/kwantummechanica> ; # Kwantummechanica
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/parabolische_differentialgleichung> ; # Parabolische Differentialgleichung
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/quasiklassische_naherung> ; # Quasiklassische Näherung
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/markov_processen> ; # Markov-processen
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/equacoes_diferenciais_parciais> ; # Equacoes diferenciais parciais
   schema:about <http://id.worldcat.org/fast/917332> ; # Evolution equations
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/schrodinger_gleichung> ; # Schrödinger-Gleichung
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/diffusievergelijkingen> ; # Diffusievergelijkingen
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/diffusionsprozess> ; # Diffusionsprozess
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/sprungprozess> ; # Sprungprozess
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/stochastische_differentialgleichung> ; # Stochastische Differentialgleichung
   schema:about <http://id.worldcat.org/fast/893561> ; # Diffusion processes
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/analyse_wiskunde> ; # Analyse (wiskunde)
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/processus_de_diffusion> ; # Processus de diffusion
   schema:about <http://experiment.worldcat.org/entity/work/data/42837#Topic/equations_d_evolution> ; # Équations d'évolution
   schema:bookFormat bgn:PrintBook ;
   schema:copyrightYear "2000" ;
   schema:creator <http://viaf.org/viaf/27305611> ; # Vasiliĭ Nikitich Kolokolʹt︠s︡ov
   schema:datePublished "2000" ;
   schema:description "Ch. 1. Gaussian diffusions. 1. Gaussian diffusion. Probabilistic and analytic approaches. 2. Classification of Gaussian diffusions by the Young schemes. 3. Long time behaviour of the Green functions of Gaussian diffusions. 4. Complex stochastic Gaussian diffusion. 5. The rate of escape for Gaussian diffusions and scattering for its perturbations -- Ch. 2. Boundary value problem for Hamiltonian systems. 1. Rapid course in calculus of variations. 2. Boundary value problem for non-degenerate Hamiltonians. 3. Regular degenerate Hamiltonians of the first rank. 4. General regular Hamiltonians depending quadratically on momenta. 5. Hamiltonians of exponential growth in momenta. 6. Complex Hamiltonians and calculus of variations of saddle-points. 7. Stochastic Hamiltonians -- Ch. 3. Semiclassical approximation for regular diffusion. 1. Main ideas of the WKB-method with imaginary phase. 2. Calculation of the two-point function for regular Hamiltonians. 3. Asymptotic solutions of the transport equation. 4. Local asymptotics of the Green function for regular Hamiltonians. 5. Global small diffusion asymptotics and large deviations. 6. Asymptotics for non-regular diffusion: an example. 7. Analytic solutions to some linear PDE -- Ch. 4. Invariant degenerate diffusion on cotangent bundles. 1. Curvilinear Ornstein-Uhlenbeck process and stochastic geodesic flow. 2. Small time asymptotics for stochastic geodesic flow. 3. The trace of the Green function and geometric invariants -- Ch. 5. Transition probability densities for stable jump-diffusion. 1. Asymptotic properties of one-dimensional stable laws. 2. Asymptotic properties of finite-dimensional stable laws. 3. Transition probability densities for stable jump-diffusion. 4. Stable jump-diffusions combined with compound Poisson processes. 5. Stable-like processes. 6. Applications to the sample path properties of stable jump-diffusions."@en ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/42837> ;
   schema:inLanguage "en" ;
   schema:isPartOf <http://worldcat.org/issn/0075-8434> ; # Lecture notes in mathematics,
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/42837#Series/lecture_notes_in_mathematics_springer_verlag> ; # Lecture notes in mathematics (Springer-Verlag) ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/654536378> ;
   schema:name "Semiclassical analysis for diffusions and stochastic processes"@en ;
   schema:productID "43555169" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/43555169#PublicationEvent/berlin_new_york_springer_2000> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/42837#Agent/springer> ; # Springer
   schema:url <http://www.springerlink.com/content/m1132137j565> ;
   schema:url <http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=1460695&custom_att_2=simple_viewer> ;
   schema:url <http://swbplus.bsz-bw.de/bsz084378603inh.htm> ;
   schema:url <http://lcweb.loc.gov/catdir/toc/00026545.html> ;
   schema:url <http://swbplus.bsz-bw.de/bsz084378603cov.htm> ;
   schema:url <http://www.springerlink.com/openurl.asp?genre=issue&issn=0075-8434&volume=1724> ;
   schema:workExample <http://worldcat.org/isbn/9783540669722> ;
   schema:workExample <http://worldcat.org/isbn/9780130281289> ;
   umbel:isLike <http://bnb.data.bl.uk/id/resource/GBA053234> ;
   umbel:isLike <http://d-nb.info/958296731> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/43555169> ;
    .


Related Entities

<http://dbpedia.org/resource/New_York_City> # New York
    a schema:Place ;
   schema:name "New York" ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Series/lecture_notes_in_mathematics_springer_verlag> # Lecture notes in mathematics (Springer-Verlag) ;
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/43555169> ; # Semiclassical analysis for diffusions and stochastic processes
   schema:name "Lecture notes in mathematics (Springer-Verlag) ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/analyse_wiskunde> # Analyse (wiskunde)
    a schema:Intangible ;
   schema:name "Analyse (wiskunde)"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/diffusievergelijkingen> # Diffusievergelijkingen
    a schema:Intangible ;
   schema:name "Diffusievergelijkingen"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/diffusionsprozess> # Diffusionsprozess
    a schema:Intangible ;
   schema:name "Diffusionsprozess"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/equacoes_diferenciais_parciais> # Equacoes diferenciais parciais
    a schema:Intangible ;
   schema:name "Equacoes diferenciais parciais"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/equations_d_evolution> # Équations d'évolution
    a schema:Intangible ;
   schema:name "Équations d'évolution"@fr ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/parabolische_differentialgleichung> # Parabolische Differentialgleichung
    a schema:Intangible ;
   schema:name "Parabolische Differentialgleichung"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/processus_de_diffusion> # Processus de diffusion
    a schema:Intangible ;
   schema:name "Processus de diffusion"@fr ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/quasiklassische_naherung> # Quasiklassische Näherung
    a schema:Intangible ;
   schema:name "Quasiklassische Näherung"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/schrodinger_gleichung> # Schrödinger-Gleichung
    a schema:Intangible ;
   schema:name "Schrödinger-Gleichung"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/42837#Topic/stochastische_differentialgleichung> # Stochastische Differentialgleichung
    a schema:Intangible ;
   schema:name "Stochastische Differentialgleichung"@en ;
    .

<http://id.worldcat.org/fast/893561> # Diffusion processes
    a schema:Intangible ;
   schema:name "Diffusion processes"@en ;
    .

<http://id.worldcat.org/fast/917332> # Evolution equations
    a schema:Intangible ;
   schema:name "Evolution equations"@en ;
    .

<http://viaf.org/viaf/27305611> # Vasiliĭ Nikitich Kolokolʹt︠s︡ov
    a schema:Person ;
   schema:familyName "Kolokolʹt︠s︡ov" ;
   schema:givenName "Vasiliĭ Nikitich" ;
   schema:givenName "V. N." ;
   schema:name "Vasiliĭ Nikitich Kolokolʹt︠s︡ov" ;
    .

<http://worldcat.org/isbn/9780130281289>
    a schema:ProductModel ;
   schema:isbn "013028128X" ;
   schema:isbn "9780130281289" ;
    .

<http://worldcat.org/isbn/9783540669722>
    a schema:ProductModel ;
   schema:isbn "3540669728" ;
   schema:isbn "9783540669722" ;
    .

<http://worldcat.org/issn/0075-8434> # Lecture notes in mathematics,
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/43555169> ; # Semiclassical analysis for diffusions and stochastic processes
   schema:issn "0075-8434" ;
   schema:name "Lecture notes in mathematics," ;
    .

<http://www.worldcat.org/oclc/654536378>
    a schema:CreativeWork ;
   rdfs:label "Semiclassical analysis for diffusions and stochastic processes." ;
   schema:description "Online version:" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/43555169> ; # Semiclassical analysis for diffusions and stochastic processes
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.