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Book Cover
E-book
Author Dalang, Robert C., 1961- author.

Title Hitting probabilities for nonlinear systems of stochastic waves / Robert C. Dalang, Marta Sanz-Solé
Published Providence, Rhode Island : American Mathematical Society, 2015
©2015

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Description 1 online resource (v, 75 pages)
Series Memoirs of the American Mathematical Society, 0065-9266 ; volume 237, number 1120
Memoirs of the American Mathematical Society ; no. 1120.
Contents Introduction -- Upper bounds on hitting probabilities -- Conditions on Malliavin matrix eigenvalues for lower bounds -- Study of Malliavin matrix eigenvalues and lower bounds -- Technical estimates -- Bibliography
Summary The authors consider a d-dimensional random field u = \{u(t, x)\} that solves a non-linear system of stochastic wave equations in spatial dimensions k \in \{1,2,3\}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent \beta. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of \mathbb{R}̂d, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that ap
Bibliography Includes bibliographical references (pages 73-75)
Notes "Volume 237, number 1120 (fourth of 6 numbers), September 2015."
Online resource; title from PDF title page (viewed October 6, 2015)
Subject Stochastic processes.
Stochastic differential equations.
Hausdorff measures.
Probabilities.
probability.
Hausdorff measures
Probabilities
Stochastic differential equations
Stochastic processes
Form Electronic book
Author Sanz Solé, Marta, 1952- author.
American Mathematical Society, publisher
ISBN 9781470425074
1470425076