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Stochastic Analysis

Edited by: Michael C. Cranston University of Rochester, Rochester, NY
Mark A. Pinsky Northwestern University, Evanston, IL
Available Formats:
Hardcover ISBN: 978-0-8218-0289-2
Product Code: PSPUM/57
621 pp
List Price: $166.00 MAA Member Price:$149.40
AMS Member Price: $132.80 Electronic ISBN: 978-0-8218-9359-3 Product Code: PSPUM/57.E 621 pp List Price:$156.00
MAA Member Price: $140.40 AMS Member Price:$124.80
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List Price: $249.00 MAA Member Price:$224.10
AMS Member Price: $199.20 Click above image for expanded view Stochastic Analysis Edited by: Michael C. Cranston University of Rochester, Rochester, NY Mark A. Pinsky Northwestern University, Evanston, IL Available Formats:  Hardcover ISBN: 978-0-8218-0289-2 Product Code: PSPUM/57 621 pp  List Price:$166.00 MAA Member Price: $149.40 AMS Member Price:$132.80
 Electronic ISBN: 978-0-8218-9359-3 Product Code: PSPUM/57.E 621 pp
 List Price: $156.00 MAA Member Price:$140.40 AMS Member Price: $124.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$249.00
MAA Member Price: $224.10 AMS Member Price:$199.20
• Book Details

Proceedings of Symposia in Pure Mathematics
Volume: 571995
MSC: Primary 34; 35; 58; 60; 82; 47; 81;

This book deals with current developments in stochastic analysis and its interfaces with partial differential equations, dynamical systems, mathematical physics, differential geometry, and infinite-dimensional analysis. The origins of stochastic analysis can be found in Norbert Wiener's construction of Brownian motion and Kiyosi Itô's subsequent development of stochastic integration and the closely related theory of stochastic (ordinary) differential equations. The papers in this volume indicate the great strides that have been made in recent years, exhibiting the tremendous power and diversity of stochastic analysis while giving a clear indication of the unsolved problems and possible future directions for development. The collection represents the proceedings of the AMS Summer Research Institute on Stochastic Analysis, held in July 1993 at Cornell University. Many of the papers are largely expository in character while containing new results.

Researchers in probability theory, partial differential equations, statistical mechanics, dynamical systems, and mathematical physics.

• Part I. Problems in analysis
• Rodrigo Bañuelos and Tom Carroll - An improvement of the Osserman constant for the bass note of a drum [ MR 1335458 ]
• M. van den Berg - Heat content asymptotics for some open sets with a fractal boundary [ MR 1335459 ]
• Erwin Bolthausen and Uwe Schmock - On self-attracting random walks [ MR 1335460 ]
• Jean Brossard - Positivity default for martingales and harmonic functions [ MR 1335461 ]
• R. Cairoli and Robert C. Dalang - Optimal switching between two Brownian motions [ MR 1335462 ]
• Z. Q. Chen, R. J. Williams and Z. Zhao - Nonnegative solutions for semilinear elliptic equations with boundary conditions—a probabilistic approach [ MR 1335463 ]
• Tzuu-Shuh Chiang and Yunshong Chow - Simulated annealing and fastest cooling rates for some $1$-dim spin glass models [ MR 1335464 ]
• Thomas G. Kurtz and Federico Marchetti - Averaging stochastically perturbed Hamiltonian systems [ MR 1335465 ]
• Terry J. Lyons - The interpretation and solution of ordinary differential equations driven by rough signals [ MR 1335466 ]
• L. C. G. Rogers - Time-reversal of the noisy Wiener-Hopf factorisation [ MR 1335467 ]
• Alain-Sol Sznitman - Some aspects of Brownian motion in a Poissonian potential [ MR 1335468 ]
• A. Truman, D. Williams and K. Y. Yu - Schrödinger operators and asymptotics for Poisson-Lévy excursion measures for one-dimensional time-homogeneous diffusions [ MR 1335469 ]
• Shinzo Watanabe - Generalized arc-sine laws for one-dimensional diffusion processes and random walks [ MR 1335470 ]
• Part II. Problems in geometry
• Hélène Airault and Paul Malliavin - Semimartingales with values in a Euclidean vector bundle and Ocone’s formula on a Riemannian manifold [ MR 1335471 ]
• Gérard Ben Arous, Michael Cranston and Wilfrid S. Kendall - Coupling constructions for hypoelliptic diffusions: two examples [ MR 1335472 ]
• Itai Benjamini, Isaac Chavel and Edgar A. Feldman - Heat kernel bounds on Riemannian manifolds [ MR 1335473 ]
• M. Brin and Yu. Kifer - Brownian motion and harmonic functions on polygonal complexes [ MR 1335474 ]
• Alexander Grigor′yan - Heat kernel of a noncompact Riemannian manifold [ MR 1335475 ]
• Elton P. Hsu - Flows and quasi-invariance of the Wiener measure on path spaces [ MR 1335476 ]
• N. Ikeda, S. Kusuoka and S. Manabe - Lévy’s stochastic area formula and related problems [ MR 1335477 ]
• Yuri Kifer - Markov processes and harmonic functions on hyperbolic metric spaces [ MR 1335478 ]
• Hiroshi Kunita - Some problems concerning Lévy processes on Lie groups [ MR 1335479 ]
• Y. Le Jan - The central limit theorem for geodesic flows on noncompact manifolds of constant negative curvature [ MR 1335480 ]
• F. Ledrappier - A renewal theorem for the distance in negative curvature [ MR 1335481 ]
• Paul Malliavin - A bootstrap proof of the limit theorem for linear SDE [ MR 1335482 ]
• Wei An Zheng - Diffusion processes on a Lipschitz Riemannian manifold and their applications [ MR 1335483 ]
• Part III. Infinite-dimensional problems
• Donald A. Dawson, Kenneth J. Hochberg and Vladimir Vinogradov - On path properties of super-2 processes. II [ MR 1335484 ]
• Bruce K. Driver - Towards calculus and geometry on path spaces [ MR 1335485 ]
• E. B. Dynkin - Branching with a single point catalyst [ MR 1335486 ]
• Jean-François Le Gall - The Brownian path-valued process and its connections with partial differential equations [ MR 1335487 ]
• Yao Zhong Hu, Tom Lindstrøm, Bernt Øksendal, Jan Ubøe and Tu Sheng Zhang - Inverse powers of white noise [ MR 1335488 ]
• H. P. McKean and K. L. Vaninsky - Statistical mechanics of nonlinear wave equations [ MR 1335489 ]
• David Nualart - Markov properties for solutions of stochastic differential equations [ MR 1335490 ]
• Ichirō Shigekawa - A quasihomeomorphism on the Wiener space [ MR 1335491 ]
• Ali Süleyman Üstünel and Moshe Zakai - Absolute continuity on the Wiener space and some applications [ MR 1335492 ]
• K. L. Vaninsky - Invariant Gibbsian measures of the Klein-Gordon equation [ MR 1335493 ]
• Part IV. Stochastic PDE/stochastic flows
• Sergio Albeverio and Michael Röckner - Dirichlet form methods for uniqueness of martingale problems and applications [ MR 1335494 ]
• Ludwig Arnold - Anticipative problems in the theory of random dynamical systems [ MR 1335495 ]
• Ludwig Arnold and Rafail Z. Khasminskii - Stability index for nonlinear stochastic differential equations [ MR 1335496 ]
• Denis R. Bell and Salah Eldin A. Mohammed - Degenerate stochastic differential equations, flows, and hypoellipticity [ MR 1335497 ]
• K. D. Elworthy and X.-M. Li - Derivative flows of stochastic differential equations: moment exponents and geometric properties [ MR 1335498 ]
• Ming Liao - Invariant diffusion processes in Lie groups and stochastic flows [ MR 1335499 ]
• R. Mikulevičius and B. L. Rozovskiĭ - On stochastic integrals in topological vector spaces [ MR 1335500 ]
• C. Mueller and R. Sowers - Travelling waves for the KPP equation with noise [ MR 1335501 ]
• Étienne Pardoux - Backward SDEs, quasilinear PDEs, and SPDEs [ MR 1335502 ]
• Mark A. Pinsky - Invariance of the Lyapunov exponent under nonlinear perturbations [ MR 1335503 ]
• Reviews

• This very rich volume … is an extremely valuable contribution to the literature on the interplay between stochastics and analysis. The editors have done a marvelous job in collecting a number of papers on subjects which in their entirety constitute the current activities in the field ... This volume has a particularly high standard and appears to be of special significance to current research activity in the ever-increasing field of stochastics and analysis.

Metrika, International Journal for Theoretical and Applied Statistics
• Request Review Copy
• Get Permissions
Volume: 571995
MSC: Primary 34; 35; 58; 60; 82; 47; 81;

This book deals with current developments in stochastic analysis and its interfaces with partial differential equations, dynamical systems, mathematical physics, differential geometry, and infinite-dimensional analysis. The origins of stochastic analysis can be found in Norbert Wiener's construction of Brownian motion and Kiyosi Itô's subsequent development of stochastic integration and the closely related theory of stochastic (ordinary) differential equations. The papers in this volume indicate the great strides that have been made in recent years, exhibiting the tremendous power and diversity of stochastic analysis while giving a clear indication of the unsolved problems and possible future directions for development. The collection represents the proceedings of the AMS Summer Research Institute on Stochastic Analysis, held in July 1993 at Cornell University. Many of the papers are largely expository in character while containing new results.

Researchers in probability theory, partial differential equations, statistical mechanics, dynamical systems, and mathematical physics.

• Part I. Problems in analysis
• Rodrigo Bañuelos and Tom Carroll - An improvement of the Osserman constant for the bass note of a drum [ MR 1335458 ]
• M. van den Berg - Heat content asymptotics for some open sets with a fractal boundary [ MR 1335459 ]
• Erwin Bolthausen and Uwe Schmock - On self-attracting random walks [ MR 1335460 ]
• Jean Brossard - Positivity default for martingales and harmonic functions [ MR 1335461 ]
• R. Cairoli and Robert C. Dalang - Optimal switching between two Brownian motions [ MR 1335462 ]
• Z. Q. Chen, R. J. Williams and Z. Zhao - Nonnegative solutions for semilinear elliptic equations with boundary conditions—a probabilistic approach [ MR 1335463 ]
• Tzuu-Shuh Chiang and Yunshong Chow - Simulated annealing and fastest cooling rates for some $1$-dim spin glass models [ MR 1335464 ]
• Thomas G. Kurtz and Federico Marchetti - Averaging stochastically perturbed Hamiltonian systems [ MR 1335465 ]
• Terry J. Lyons - The interpretation and solution of ordinary differential equations driven by rough signals [ MR 1335466 ]
• L. C. G. Rogers - Time-reversal of the noisy Wiener-Hopf factorisation [ MR 1335467 ]
• Alain-Sol Sznitman - Some aspects of Brownian motion in a Poissonian potential [ MR 1335468 ]
• A. Truman, D. Williams and K. Y. Yu - Schrödinger operators and asymptotics for Poisson-Lévy excursion measures for one-dimensional time-homogeneous diffusions [ MR 1335469 ]
• Shinzo Watanabe - Generalized arc-sine laws for one-dimensional diffusion processes and random walks [ MR 1335470 ]
• Part II. Problems in geometry
• Hélène Airault and Paul Malliavin - Semimartingales with values in a Euclidean vector bundle and Ocone’s formula on a Riemannian manifold [ MR 1335471 ]
• Gérard Ben Arous, Michael Cranston and Wilfrid S. Kendall - Coupling constructions for hypoelliptic diffusions: two examples [ MR 1335472 ]
• Itai Benjamini, Isaac Chavel and Edgar A. Feldman - Heat kernel bounds on Riemannian manifolds [ MR 1335473 ]
• M. Brin and Yu. Kifer - Brownian motion and harmonic functions on polygonal complexes [ MR 1335474 ]
• Alexander Grigor′yan - Heat kernel of a noncompact Riemannian manifold [ MR 1335475 ]
• Elton P. Hsu - Flows and quasi-invariance of the Wiener measure on path spaces [ MR 1335476 ]
• N. Ikeda, S. Kusuoka and S. Manabe - Lévy’s stochastic area formula and related problems [ MR 1335477 ]
• Yuri Kifer - Markov processes and harmonic functions on hyperbolic metric spaces [ MR 1335478 ]
• Hiroshi Kunita - Some problems concerning Lévy processes on Lie groups [ MR 1335479 ]
• Y. Le Jan - The central limit theorem for geodesic flows on noncompact manifolds of constant negative curvature [ MR 1335480 ]
• F. Ledrappier - A renewal theorem for the distance in negative curvature [ MR 1335481 ]
• Paul Malliavin - A bootstrap proof of the limit theorem for linear SDE [ MR 1335482 ]
• Wei An Zheng - Diffusion processes on a Lipschitz Riemannian manifold and their applications [ MR 1335483 ]
• Part III. Infinite-dimensional problems
• Donald A. Dawson, Kenneth J. Hochberg and Vladimir Vinogradov - On path properties of super-2 processes. II [ MR 1335484 ]
• Bruce K. Driver - Towards calculus and geometry on path spaces [ MR 1335485 ]
• E. B. Dynkin - Branching with a single point catalyst [ MR 1335486 ]
• Jean-François Le Gall - The Brownian path-valued process and its connections with partial differential equations [ MR 1335487 ]
• Yao Zhong Hu, Tom Lindstrøm, Bernt Øksendal, Jan Ubøe and Tu Sheng Zhang - Inverse powers of white noise [ MR 1335488 ]
• H. P. McKean and K. L. Vaninsky - Statistical mechanics of nonlinear wave equations [ MR 1335489 ]
• David Nualart - Markov properties for solutions of stochastic differential equations [ MR 1335490 ]
• Ichirō Shigekawa - A quasihomeomorphism on the Wiener space [ MR 1335491 ]
• Ali Süleyman Üstünel and Moshe Zakai - Absolute continuity on the Wiener space and some applications [ MR 1335492 ]
• K. L. Vaninsky - Invariant Gibbsian measures of the Klein-Gordon equation [ MR 1335493 ]
• Part IV. Stochastic PDE/stochastic flows
• Sergio Albeverio and Michael Röckner - Dirichlet form methods for uniqueness of martingale problems and applications [ MR 1335494 ]
• Ludwig Arnold - Anticipative problems in the theory of random dynamical systems [ MR 1335495 ]
• Ludwig Arnold and Rafail Z. Khasminskii - Stability index for nonlinear stochastic differential equations [ MR 1335496 ]
• Denis R. Bell and Salah Eldin A. Mohammed - Degenerate stochastic differential equations, flows, and hypoellipticity [ MR 1335497 ]
• K. D. Elworthy and X.-M. Li - Derivative flows of stochastic differential equations: moment exponents and geometric properties [ MR 1335498 ]
• Ming Liao - Invariant diffusion processes in Lie groups and stochastic flows [ MR 1335499 ]
• R. Mikulevičius and B. L. Rozovskiĭ - On stochastic integrals in topological vector spaces [ MR 1335500 ]
• C. Mueller and R. Sowers - Travelling waves for the KPP equation with noise [ MR 1335501 ]
• Étienne Pardoux - Backward SDEs, quasilinear PDEs, and SPDEs [ MR 1335502 ]
• Mark A. Pinsky - Invariance of the Lyapunov exponent under nonlinear perturbations [ MR 1335503 ]
• This very rich volume … is an extremely valuable contribution to the literature on the interplay between stochastics and analysis. The editors have done a marvelous job in collecting a number of papers on subjects which in their entirety constitute the current activities in the field ... This volume has a particularly high standard and appears to be of special significance to current research activity in the ever-increasing field of stochastics and analysis.

Metrika, International Journal for Theoretical and Applied Statistics
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