 On a class of exponential changes of measure for stochastic PDEsThorben Pieper-Sethmacher, Frank van der Meulen and Aad van der Vaart Stochastic Processes and their Applications, 2025, vol. 185, issue C Abstract: Given a mild solution X to a semilinear stochastic partial differential equation (SPDE), we consider an exponential change of measure based on its infinitesimal generator L, defined in the topology of bounded pointwise convergence. The changed measure Ph depends on the choice of a function h in the domain of L. In our main result, we derive conditions on h for which the change of measure is of Girsanov-type. The process X under Ph is then shown to be a mild solution to another SPDE with an extra additive drift-term. We illustrate how different choices of h impact the law of X under Ph in selected applications. These include the derivation of an infinite-dimensional diffusion bridge as well as the introduction of guided processes for SPDEs, generalizing results known for finite-dimensional diffusion processes to the infinite-dimensional case. Keywords: Doob’s h-transform; Exponential change of measure; Girsanov theorem; Guided process; Infinite-dimensional diffusion bridge; Kolmogorov operator; Pinned process; Semilinear SPDE; SPDE bridge (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:185:y:2025:i:c:s0304414925000717 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2025.104630 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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