Hitting probabilities for nonlinear systems of stochastic waves. Memoirs of the American Mathematical Society; 1120 = Vol. 237,4.

Dalang, Robert C.; Sanz-Sole, Marta

ISBN 10: 1470414236 / ISBN 13: 9781470414238

Edité par Providence, American Math. Soc, 2015

A propos de cet article

Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-00422 9781470414238 Sprache: Englisch Gewicht in Gramm: 150.

N° de réf. du vendeur 2482933

Détails bibliographiques

• Titre: Hitting probabilities for nonlinear systems of stochastic waves. Memoirs of the American Mathematical Society; 1120 = Vol. 237,4.
• Éditeur: Providence, American Math. Soc
• Date de parution: 2015
• Langue: anglais
• ISBN à 10 chiffres: 1470414236
• ISBN à 13 chiffres: 9781470414238
• Reliure: Softcover
• Catalogues du vendeur:
  • SA MATHEMATIK

A propos de ce titre

Synopsis

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.

À propos de l?auteur

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

Marta Sanz-Sole, University of Barcelona, Spain.