Hitting Probabilities for Nonlinear Systems of Stochastic Waves (Memoirs of the American Mathematical Society, Band 237) - Softcover

Dalang, Robert C.; Sanz-Sole, Marta

 
9781470414238: Hitting Probabilities for Nonlinear Systems of Stochastic Waves (Memoirs of the American Mathematical Society, Band 237)
Softcover
ISBN 10: 1470414236 ISBN 13: 9781470414238
Verlag: American Mathematical Society, 2015

Inhaltsangabe

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 appears in the Hausdorff measure is close to optimal, and shows that when $d(2-\beta) > 2(k+1)$, points are polar for $u$. Conversely, in low dimensions $d$, points are not polar. There is, however, an interval in which the question of polarity of points remains open.

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Über die Autorin bzw. den Autor

Robert C. Dalang, Ecole Polytechnique Federale de Lausanne, Switzerland, and University of Barcelona, Spain.

Marta Sanz-Sole, University of Barcelona, Spain.

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Verlag
American Mathematical Society
Erscheinungsdatum
2015
Sprache
Englisch
ISBN 10 
1470414236
ISBN 13 
9781470414238
Einband
Taschenbuch
Anzahl der Seiten
75
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Verantwortliche Person
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