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E-grāmata: Geometry of Random Motion

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  • Formāts: 337 pages
  • Sērija : Contemporary Mathematics No. 73
  • Izdošanas datums: 11-Jan-2011
  • Izdevniecība: American Mathematical Society
  • ISBN-13: 9780821876626
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Geometry of Random Motion
  • Formāts: 337 pages
  • Sērija : Contemporary Mathematics No. 73
  • Izdošanas datums: 11-Jan-2011
  • Izdevniecība: American Mathematical Society
  • ISBN-13: 9780821876626
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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.
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.
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