| eBook ISBN: | 978-0-8218-7662-6 |
| Product Code: | CONM/73.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| eBook ISBN: | 978-0-8218-7662-6 |
| Product Code: | CONM/73.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
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Book DetailsContemporary MathematicsVolume: 73; 1988; 337 ppMSC: Primary 58
In July 1987, an AMS-IMS-SIAM Joint Summer Research Conference on Geometry of Random Motion was held at Cornell University. The initial impetus for the meeting came from the desire to further explore the now-classical connection between diffusion processes and second-order (hypo)elliptic differential operators. To accomplish this goal, the conference brought together leading researchers with varied backgrounds and interests: probabilists who have proved results in geometry, geometers who have used probabilistic methods, and probabilists who have studied diffusion processes.
Focusing on the interplay between probability and differential geometry, this volume examines diffusion processes on various geometric structures, such as Riemannian manifolds, Lie groups, and symmetric spaces. Some of the articles specifically address analysis on manifolds, while others center on (nongeometric) stochastic analysis. The majority of the articles deal simultaneously with probabilistic and geometric techniques.
Requiring a knowledge of the modern theory of diffusion processes, this book will appeal to mathematicians, mathematical physicists, and other researchers interested in Brownian motion, diffusion processes, Laplace-Beltrami operators, and the geometric applications of these concepts. The book provides a detailed view of the leading edge of research in this rapidly moving field.
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Table of Contents
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Articles
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Isaac Chavel, Edgar Feldman and Jay Rosen — Fluctuations of the Wiener sausage for surfaces [ MR 954623 ]
-
M. Cranston and C. Mueller — A review of recent and older results on the absolute continuity of harmonic measure [ MR 954624 ]
-
R. W. R. Darling — Constructing stochastic flows: some examples [ MR 954625 ]
-
Jozef Dodziuk and Leon Karp — Spectral and function theory for combinatorial Laplacians [ MR 954626 ]
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Peter G. Doyle — On deciding whether a surface is parabolic or hyperbolic [ MR 954627 ]
-
T. E. Duncan — A solvable stochastic control problem in spheres [ MR 954628 ]
-
K. D. Elworthy — Brownian motion and the ends of a manifold [ MR 954629 ]
-
Masatoshi Fukushima — On holomorphic diffusions and plurisubharmonic functions [ MR 954630 ]
-
Peter B. Gilkey — Leading terms in the asymptotics of the heat equation [ MR 954631 ]
-
Joseph Glover — Probability and differential equations [ MR 954632 ]
-
Pei Hsu — Brownian motion and Riemannian geometry [ MR 954633 ]
-
Leon Karp and Mark Pinsky — First-order asymptotics of the principal eigenvalue of tubular neighborhoods [ MR 954634 ]
-
Wilfrid S. Kendall — Martingales on manifolds and harmonic maps [ MR 954635 ]
-
Yuri Kifer — Harmonic functions on Riemannian manifolds [ MR 954636 ]
-
Rémi Léandre — Quantitative and geometric applications of the Malliavin calculus [ MR 954637 ]
-
Ming Liao — An independence property of Riemannian Brownian motions [ MR 954638 ]
-
Ming Liao and Mark Pinsky — Stochastic parallel translation for Riemannian Brownian motion conditioned to hit a fixed point of a sphere [ MR 954639 ]
-
Peter March — Probabilistic interpretation of Hadamard’s variational formulas [ MR 954640 ]
-
Carl Mueller — A counterexample for Brownian motion on manifolds [ MR 954641 ]
-
Bernt Øksendal — Using random motion to study quasiregular functions [ MR 954642 ]
-
E. J. Pauwels and L. C. G. Rogers — Skew-product decompositions of Brownian motions [ MR 954643 ]
-
Mark Pinsky — Local stochastic differential geometry, or What can you learn about a manifold by watching Brownian motion? [ MR 954644 ]
-
Ross Pinsky — Transience and recurrence for multidimensional diffusions: a survey and a recent result [ MR 954645 ]
-
Steven Rosenberg — Semigroup domination and vanishing theorems [ MR 954646 ]
-
J. C. Taylor — The Iwasawa decomposition and the limiting behaviour of Brownian motion on a symmetric space of noncompact type [ MR 954647 ]
-
N. Th. Varopoulos — Green’s function and harmonic functions on manifolds [ MR 954648 ]
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In July 1987, an AMS-IMS-SIAM Joint Summer Research Conference on Geometry of Random Motion was held at Cornell University. The initial impetus for the meeting came from the desire to further explore the now-classical connection between diffusion processes and second-order (hypo)elliptic differential operators. To accomplish this goal, the conference brought together leading researchers with varied backgrounds and interests: probabilists who have proved results in geometry, geometers who have used probabilistic methods, and probabilists who have studied diffusion processes.
Focusing on the interplay between probability and differential geometry, this volume examines diffusion processes on various geometric structures, such as Riemannian manifolds, Lie groups, and symmetric spaces. Some of the articles specifically address analysis on manifolds, while others center on (nongeometric) stochastic analysis. The majority of the articles deal simultaneously with probabilistic and geometric techniques.
Requiring a knowledge of the modern theory of diffusion processes, this book will appeal to mathematicians, mathematical physicists, and other researchers interested in Brownian motion, diffusion processes, Laplace-Beltrami operators, and the geometric applications of these concepts. The book provides a detailed view of the leading edge of research in this rapidly moving field.
-
Articles
-
Isaac Chavel, Edgar Feldman and Jay Rosen — Fluctuations of the Wiener sausage for surfaces [ MR 954623 ]
-
M. Cranston and C. Mueller — A review of recent and older results on the absolute continuity of harmonic measure [ MR 954624 ]
-
R. W. R. Darling — Constructing stochastic flows: some examples [ MR 954625 ]
-
Jozef Dodziuk and Leon Karp — Spectral and function theory for combinatorial Laplacians [ MR 954626 ]
-
Peter G. Doyle — On deciding whether a surface is parabolic or hyperbolic [ MR 954627 ]
-
T. E. Duncan — A solvable stochastic control problem in spheres [ MR 954628 ]
-
K. D. Elworthy — Brownian motion and the ends of a manifold [ MR 954629 ]
-
Masatoshi Fukushima — On holomorphic diffusions and plurisubharmonic functions [ MR 954630 ]
-
Peter B. Gilkey — Leading terms in the asymptotics of the heat equation [ MR 954631 ]
-
Joseph Glover — Probability and differential equations [ MR 954632 ]
-
Pei Hsu — Brownian motion and Riemannian geometry [ MR 954633 ]
-
Leon Karp and Mark Pinsky — First-order asymptotics of the principal eigenvalue of tubular neighborhoods [ MR 954634 ]
-
Wilfrid S. Kendall — Martingales on manifolds and harmonic maps [ MR 954635 ]
-
Yuri Kifer — Harmonic functions on Riemannian manifolds [ MR 954636 ]
-
Rémi Léandre — Quantitative and geometric applications of the Malliavin calculus [ MR 954637 ]
-
Ming Liao — An independence property of Riemannian Brownian motions [ MR 954638 ]
-
Ming Liao and Mark Pinsky — Stochastic parallel translation for Riemannian Brownian motion conditioned to hit a fixed point of a sphere [ MR 954639 ]
-
Peter March — Probabilistic interpretation of Hadamard’s variational formulas [ MR 954640 ]
-
Carl Mueller — A counterexample for Brownian motion on manifolds [ MR 954641 ]
-
Bernt Øksendal — Using random motion to study quasiregular functions [ MR 954642 ]
-
E. J. Pauwels and L. C. G. Rogers — Skew-product decompositions of Brownian motions [ MR 954643 ]
-
Mark Pinsky — Local stochastic differential geometry, or What can you learn about a manifold by watching Brownian motion? [ MR 954644 ]
-
Ross Pinsky — Transience and recurrence for multidimensional diffusions: a survey and a recent result [ MR 954645 ]
-
Steven Rosenberg — Semigroup domination and vanishing theorems [ MR 954646 ]
-
J. C. Taylor — The Iwasawa decomposition and the limiting behaviour of Brownian motion on a symmetric space of noncompact type [ MR 954647 ]
-
N. Th. Varopoulos — Green’s function and harmonic functions on manifolds [ MR 954648 ]
