Potential theory for hyperbolic SPDEs

Mostra el registre complet Registre parcial de l'ítem

• dc.contributor.author Dalang, Robert C.ca
• dc.contributor.author Nualart, Eulàliaca
• dc.date.accessioned 2018-04-18T08:31:03Z
• dc.date.available 2018-04-18T08:31:03Z
• dc.date.issued 2004
• dc.description.abstract We give general sufficient conditions which imply upper and lower bounds for the probability that a multiparameter process hits a given set E in terms of a capacity of E related to the process. This extends a result of Khoshnevisan and Shi [Ann. Probab. 27 (1999) 1135–1159], where estimates for the hitting probabilities of the (N,d) Brownian sheet in terms of the (d−2N) Newtonian capacity are obtained, and readily applies to a wide class of Gaussian processes. Using Malliavin calculus and, in particular, a result of Kohatsu-Higa [Probab. Theory Related Fields 126 (2003) 421–457], we apply these general results to the solution of a system of d nonlinear hyperbolic stochastic partial differential equations with two variables. We show that under standard hypotheses on the coefficients, the hitting probabilities of this solution are bounded above and below by constants times the (d−4) Newtonian capacity. As a consequence, we characterize polar sets for this process and prove that the Hausdorff dimension of its range is min (d,4) a.s.en
• dc.description.sponsorship Supported in part by the Swiss National Foundation for Scientific Research.
• dc.format.mimetype application/pdf
• dc.identifier.citation Dalang RC, Nualart E. Potential theory for hyperbolic SPDEs. Ann Probab. 2004;32(3):2099-148. DOI: 10.1214/009117904000000685
• dc.identifier.doi http://dx.doi.org/10.1214/009117904000000685
• dc.identifier.issn 0091-1798
• dc.identifier.uri http://hdl.handle.net/10230/34387
• dc.language.iso eng
• dc.publisher Institute of Mathematical Statistics (IMS)ca
• dc.relation.ispartof The Annals of Probability. 2004;32(3):2099-148.
• dc.rights © Institute of Mathematical Statistics, 2004
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Potential theoryen
• dc.subject.keyword Nonlinear hyperbolic SPDEen
• dc.subject.keyword Multiparameter processen
• dc.subject.keyword Gaussian processen
• dc.subject.keyword Hitting probabilityen
• dc.title Potential theory for hyperbolic SPDEsca
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion