McKean, Henry P. (Henry Pratt) 1930
Overview
Works:  49 works in 195 publications in 4 languages and 3,814 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor, Honoree, Contributor, Dedicatee 
Classifications:  QA273, 515.2433 
Publication Timeline
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Most widely held works about
Henry P McKean
 Mckean, Henry P.: mathematics ( )
 Henry Pratt McKean by Zeta Psi FraternityZeta Psi Fraternity( )
Most widely held works by
Henry P McKean
Diffusion processes and their sample paths
by
Kiyosi Itō(
Book
)
40 editions published between 1964 and 2010 in English and German and held by 809 WorldCat member libraries worldwide
40 editions published between 1964 and 2010 in English and German and held by 809 WorldCat member libraries worldwide
Fourier series and integrals
by
H Dym(
Book
)
23 editions published between 1972 and 2003 in English and held by 759 WorldCat member libraries worldwide
23 editions published between 1972 and 2003 in English and held by 759 WorldCat member libraries worldwide
Stochastic integrals
by
Henry P McKean(
Book
)
25 editions published between 1969 and 2014 in 3 languages and held by 660 WorldCat member libraries worldwide
25 editions published between 1969 and 2014 in 3 languages and held by 660 WorldCat member libraries worldwide
Elliptic curves : function theory, geometry, arithmetic
by
Henry P McKean(
Book
)
23 editions published between 1997 and 2007 in English and held by 538 WorldCat member libraries worldwide
The subject of elliptic curves is one of the jewels of nineteenthcentury mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. The treatment combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetics. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics. The many exercises with hints scattered throughout the text give the reader a glimpse of further developments
23 editions published between 1997 and 2007 in English and held by 538 WorldCat member libraries worldwide
The subject of elliptic curves is one of the jewels of nineteenthcentury mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. The treatment combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetics. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics. The many exercises with hints scattered throughout the text give the reader a glimpse of further developments
Gaussian processes, function theory, and the inverse spectral problem
by
H Dym(
Book
)
12 editions published between 1975 and 2008 in English and held by 441 WorldCat member libraries worldwide
12 editions published between 1975 and 2008 in English and held by 441 WorldCat member libraries worldwide
Stochastic differential equations
by Symposium in Applied Mathematics: Stochastic Differential Equations(
Book
)
8 editions published in 1973 in English and held by 342 WorldCat member libraries worldwide
8 editions published in 1973 in English and held by 342 WorldCat member libraries worldwide
Probability, geometry, and integrable systems : for Henry McKean's seventyfifth birthday
by
Mark A Pinsky(
Book
)
7 editions published between 2008 and 2011 in English and held by 177 WorldCat member libraries worldwide
7 editions published between 2008 and 2011 in English and held by 177 WorldCat member libraries worldwide
Diffusion Processes and their Sample Paths Reprint of the 1974 Edition
by
Kiyosi Itō(
)
2 editions published between 1965 and 1996 in English and held by 20 WorldCat member libraries worldwide
U4 = Reihentext + Werbetext für dieses Buch Werbetext: Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one or more dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean
2 editions published between 1965 and 1996 in English and held by 20 WorldCat member libraries worldwide
U4 = Reihentext + Werbetext für dieses Buch Werbetext: Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one or more dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean
Probability : the classical limit theorems
by
Henry P McKean(
Book
)
2 editions published in 2014 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 2014 in English and held by 9 WorldCat member libraries worldwide
Diffuzionnye processy i ich traektorii
by
Kiyosi Itō(
Book
)
3 editions published in 1968 in Russian and held by 5 WorldCat member libraries worldwide
3 editions published in 1968 in Russian and held by 5 WorldCat member libraries worldwide
Stochastičeskie integraly
by
Henry P McKean(
Book
)
1 edition published in 1972 in Russian and held by 3 WorldCat member libraries worldwide
1 edition published in 1972 in Russian and held by 3 WorldCat member libraries worldwide
Universal symplectic forms in the soliton theory
by Fedor Soloviev(
Book
)
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
Using KricheverPhong's universal formula, we show that a multiplicative representation linearizes Sklyanian quadratic brackets for a multipole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a byproduct, we obtain an extension of a Sklyanin algebra in the elliptic case. We discuss applications of these results to isospectral and isomonodromic equations with discrete time. KricheverPhong's formula provides a hierarchy of symplectic structures, and we show that there exists a nontrivial cubic bracket in Sklyanin's case. Also, we consider a generalization of the universal formula to variable base curves (suggested in [22]) in the simplest possible case of a rational base curve with moving marked points
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
Using KricheverPhong's universal formula, we show that a multiplicative representation linearizes Sklyanian quadratic brackets for a multipole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a byproduct, we obtain an extension of a Sklyanin algebra in the elliptic case. We discuss applications of these results to isospectral and isomonodromic equations with discrete time. KricheverPhong's formula provides a hierarchy of symplectic structures, and we show that there exists a nontrivial cubic bracket in Sklyanin's case. Also, we consider a generalization of the universal formula to variable base curves (suggested in [22]) in the simplest possible case of a rational base curve with moving marked points
The nonlinear Schroedinger equation with a delta potential and even initial data
by Jungwoon Park(
Book
)
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
Among a number of different ways to solve the IBV problem, we follow the method of Bikbaev and Tarasov which utilizes a Backlund transformation to extend the solution on the halfline to a solution of the NLS equation on the whole line, in such a way that the boundary condition is automatically satisfied. The long time asymptotics for the solutions of the equation can then be obtained by the nonlinear steepestdescent method for RiemannHilbert problems introduced by Deift and Zhou
2 editions published in 2010 in English and held by 2 WorldCat member libraries worldwide
Among a number of different ways to solve the IBV problem, we follow the method of Bikbaev and Tarasov which utilizes a Backlund transformation to extend the solution on the halfline to a solution of the NLS equation on the whole line, in such a way that the boundary condition is automatically satisfied. The long time asymptotics for the solutions of the equation can then be obtained by the nonlinear steepestdescent method for RiemannHilbert problems introduced by Deift and Zhou
A free boundary problem for the heat equation arising from a problem of mathematical economics
by
Henry P McKean(
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
Large deviation lower bounds for the totally asymmetric simple exclusion process
by Yevgeny Vilensky(
Book
)
2 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
The totally asymmetric simple exclusion process (TASEP) has been shown to have a hydrodynamic scaling limit under the hyperbolic scaling of space and time. This limit is a measure, whose density with respect to Lebesgue measure is given by the unique entropy weak solution to a nonlinear partial differential equation in conservation form. Large deviations for this problem had been studied by Jensen in his thesis, who proved the upper bound and obtained a lower bound result for nonentropic weak solutions that are constant away from a single line of constant speed [3]. The subject of this thesis is the extension of the lower bound result to a wider class of nonentropic weak solutions. In particular, we show that for weak solutions that are entropic away from smooth curves and which have sufficient regularity, the lower bound holds. We prove locality results that show that the entropy of a modified TASEP (relative to a standard TASEP), with modifications applied locally at macroscopically separated sites, can be decomposed into the sum, over all such sites, of the relative entropies of TASEPs with just one modification
2 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
The totally asymmetric simple exclusion process (TASEP) has been shown to have a hydrodynamic scaling limit under the hyperbolic scaling of space and time. This limit is a measure, whose density with respect to Lebesgue measure is given by the unique entropy weak solution to a nonlinear partial differential equation in conservation form. Large deviations for this problem had been studied by Jensen in his thesis, who proved the upper bound and obtained a lower bound result for nonentropic weak solutions that are constant away from a single line of constant speed [3]. The subject of this thesis is the extension of the lower bound result to a wider class of nonentropic weak solutions. In particular, we show that for weak solutions that are entropic away from smooth curves and which have sufficient regularity, the lower bound holds. We prove locality results that show that the entropy of a modified TASEP (relative to a standard TASEP), with modifications applied locally at macroscopically separated sites, can be decomposed into the sum, over all such sites, of the relative entropies of TASEPs with just one modification
Harmonic functions for random walks in random environments
by Paris Pender(
Book
)
2 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
We consider random walks in stationary ergodic random environments. In the case of uniformly elliptic walks, we prove the existence of quenched harmonic functions of the form etheta·x+f (x) for some sublinear f, and a specific class of theta. We then move to a spacetime environment and prove minimality theorems for such functions in a special case
2 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
We consider random walks in stationary ergodic random environments. In the case of uniformly elliptic walks, we prove the existence of quenched harmonic functions of the form etheta·x+f (x) for some sublinear f, and a specific class of theta. We then move to a spacetime environment and prove minimality theorems for such functions in a special case
My methods in breeding poultry
by
Henry P McKean(
Book
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
Advances in mathematics. Edited by GianCarlo Rota
(
Book
)
in Undetermined and English and held by 2 WorldCat member libraries worldwide
in Undetermined and English and held by 2 WorldCat member libraries worldwide
Randomly trapped random walks
by Roman Royfman(
Book
)
2 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
The model introduced in this work model, Randomly Trapped Random Walk (RTRW), is a general framework to study a onedimensional motion in a random trapping environment. We develop tools to study its scaling limits. We discover that all possible limits of RTRW can be represented as a Brownian motion timechanged by a Levy subordinator. More precisely, we will show that if the trapping landscape is homogeneous, RTRW exhibits diffusive behavior. On the other hand, in inhomogeneous environments, RTRW is nondiffusive. The set of possible limits of RTRW (in inhomogeneous environments) is extremely rich. In particular, it includes Fractional Kinetics, which was initially introduced as a scaling limit of Continuous Time Random Walk, as well as a new broad class of processes, which we call Randomly Trapped Brownian Motions. This class contains a singular diffusion, which was recently introduced by Fontes, Isopi and Newman. We give various examples, some of the of a geometric nature, i.e. the Comb Model
2 editions published in 2008 in English and held by 2 WorldCat member libraries worldwide
The model introduced in this work model, Randomly Trapped Random Walk (RTRW), is a general framework to study a onedimensional motion in a random trapping environment. We develop tools to study its scaling limits. We discover that all possible limits of RTRW can be represented as a Brownian motion timechanged by a Levy subordinator. More precisely, we will show that if the trapping landscape is homogeneous, RTRW exhibits diffusive behavior. On the other hand, in inhomogeneous environments, RTRW is nondiffusive. The set of possible limits of RTRW (in inhomogeneous environments) is extremely rich. In particular, it includes Fractional Kinetics, which was initially introduced as a scaling limit of Continuous Time Random Walk, as well as a new broad class of processes, which we call Randomly Trapped Brownian Motions. This class contains a singular diffusion, which was recently introduced by Fontes, Isopi and Newman. We give various examples, some of the of a geometric nature, i.e. the Comb Model
Marking the (1,2) points of the Brownian web and applications
by
Emmanuel Schertzer(
Book
)
2 editions published in 2007 in English and held by 2 WorldCat member libraries worldwide
The Brownian web (BW), which developed from the work of Arratia and then Toth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional spacetime that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the Brownian net (BN) constructed by Sun and Swart, and the dynamical Brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits of corresponding discrete extensions of the DWthe discrete net (DN) and the dynamical discrete web (DyDW). These discrete extensions have a natural geometric structure in which the underlying Bernoulli left or right "arrow" structure of the DW is extended by means of branching (i.e., allowing left and right simultaneously) to construct the DN or by means of switching (i.e., from left to right and viceversa) to construct the DyDW. We show that there is a similar structure in the continuum where arrow direction is replaced by the left or right parity of the (1, 2) spacetime points of the BW (points with one incoming path from the past and two outgoing paths to the future, only one of which is a continuation of the incoming path). We then provide a complete construction of the DyBW and an alternate construction of the BN to that of Sun and Swart by proving that the switching or branching can be implemented by a Poissonian marking of the (1, 2) points. Beyond the BN and the DyBW, we apply our marking technology to construct two other continuum objects. One is the scaling limit of a variation of the onedimensional stochastics Potts model at low temperature (the boundary nucleation model). The second is a class of stochastic flows of kernels that can be interpreted as diffusions in a random medium
2 editions published in 2007 in English and held by 2 WorldCat member libraries worldwide
The Brownian web (BW), which developed from the work of Arratia and then Toth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional spacetime that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the Brownian net (BN) constructed by Sun and Swart, and the dynamical Brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits of corresponding discrete extensions of the DWthe discrete net (DN) and the dynamical discrete web (DyDW). These discrete extensions have a natural geometric structure in which the underlying Bernoulli left or right "arrow" structure of the DW is extended by means of branching (i.e., allowing left and right simultaneously) to construct the DN or by means of switching (i.e., from left to right and viceversa) to construct the DyDW. We show that there is a similar structure in the continuum where arrow direction is replaced by the left or right parity of the (1, 2) spacetime points of the BW (points with one incoming path from the past and two outgoing paths to the future, only one of which is a continuation of the incoming path). We then provide a complete construction of the DyBW and an alternate construction of the BN to that of Sun and Swart by proving that the switching or branching can be implemented by a Poissonian marking of the (1, 2) points. Beyond the BN and the DyBW, we apply our marking technology to construct two other continuum objects. One is the scaling limit of a variation of the onedimensional stochastics Potts model at low temperature (the boundary nucleation model). The second is a class of stochastic flows of kernels that can be interpreted as diffusions in a random medium
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Related Identities
 Dym, H. (Harry) 1938 Author
 Itō, Kiyosi 19152008 Author
 Moll, Victor H. 1956
 Keller, Joseph B. (Joseph Bishop) 1923 Editor
 American Mathematical Society Other
 Society for Industrial and Applied Mathematics Other
 Pinsky, Mark A. 1940 Editor
 Birnir, Björn Editor
 Ben Arous, Gerard
 Sheffield, Scott
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Associated Subjects
Brownian motion processes Brownian movements Canada Curves, Elliptic Diffusion Diffusion processes Distribution (Probability theory) Fourier series Gaussian processes Geometry, Algebraic Geometry, Differential Hamiltonian systems Limit theorems (Probability theory) Mathematics PoultryBreeding Prediction theory Probabilities Scientists Spectral theory (Mathematics) Stationary processes Stochastic differential equations Stochastic integrals Stochastic processes United States
Alternative Names
Mac Kean, Henry P.
Mac Kean Henry P. 1930....
MacKean, Henry P.
MacKean Henry P. 1930....
Makkin, G.
Makkin, G. 1930
Mc Kean, Henry P.
Mc Kean Henry P. 1930....
McKean, H. P.
McKean, H. P. 1930
McKean, H. P. 1930 Jr
McKean, H. P. (Henry P.)
McKean, H. P. (Henry P.), 1930
McKean, H. P. (Henry P.), Jr., 1930
McKean, H. P. Jr
McKean, Henry
McKean, Henry 1930
McKean, Henry P.
McKean, Henry P. Jr
Маккин, Г
Маккин, Г. (Генри П.)
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