Description |
1 online resource (v, 75 pages) |
Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 237, number 1120 |
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Memoirs of the American Mathematical Society ; no. 1120.
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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." |
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Online resource; title from PDF title page (viewed October 6, 2015) |
Subject |
Stochastic processes.
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Stochastic differential equations.
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Hausdorff measures.
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Probabilities.
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probability.
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Hausdorff measures
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Probabilities
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Stochastic differential equations
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Stochastic processes
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Form |
Electronic book
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Author |
Sanz Solé, Marta, 1952- author.
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American Mathematical Society, publisher
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ISBN |
9781470425074 |
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1470425076 |
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