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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978-0-8218-5081-7 (9780821850817)
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Schweitzer Klassifikation
Fluctuations of the Wiener sausage for surfaces by I. Chavel, E. Feldman, and J. Rosen A review of recent and older results on the absolute continuity of harmonic measure by M. Cranston and C. Mueller Constructing stochastic flows: some examples by R. W. R. Darling Spectral and function theory for combinatorial laplacians by J. Dodziuk and L. Karp On deciding whether a surface is parabolic or hyperbolic by P. G. Doyle A solvable stochastic control problem in spheres by T. E. Duncan Brownian motion and the ends of a manifold by K. D. Elworthy On holomorphic diffusions and plurisubharmonic functions by M. Fukushima Leading terms in the asymptotic expansion of the heat equation by P. B. Gilkey Probability theory and differential equations by J. Glover Brownian motion and Riemannian geometry by P. Hsu First-order asymptotics of the principal eigenvalue of tubular neighborhoods by L. Karp and M. Pinsky Martingales on manifolds and harmonic maps by W. Kendall Harmonic functions on Riemannian manifolds by Y. Kifer Quantitative and geometric applications of the Malliavin calculus by R. Leandre An independence property of Brownian motion by M. Liao Stochastic parallel translation for Riemannian Brownian motion conditioned to hit a fixed point of a sphere by M. Liao and M. Pinsky Probabilistic interpretation of Hadamard's variational formula by P. March A counterexample for Brownian motion on manifolds by C. Mueller Using Brownian motion to study quasi-regular functions by B. Oksendal Skew-product decompositions of Brownian motions by E. J. Pauwels and L. C. G. Rogers Local stochastic differential geometry by M. Pinsky Transience and recurrence for multidimensional diffusions: a survey and a recent result by R. Pinsky Semigroup domination and vanishing theorems by S. Rosenberg The Iwasa decomposition and the limiting behavior of Brownian motion on a symmetric space of noncompact type by J. C. Taylor Green's functions and harmonic functions on manifolds by N. Th. Varopoulos.
