Probabilistic Representations of Solutions of the Forward Equations

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dc.creatorRajeev, B.
dc.creatorThangavelu, S.
dc.date2007-06-22
dc.date.accessioned2026-07-07T08:11:55Z
dc.date.available2026-07-07T08:11:55Z
dc.descriptionIn this paper we prove a stochastic representation for solutions of the evolution equation $ \partial_t ψ_t = {1/2}L^*ψ_t $ where $ L^* $ is the formal adjoint of an elliptic second order differential operator with smooth coefficients corresponding to the infinitesimal generator of a finite dimensional diffusion $ (X_t).$ Given $ ψ_0 = ψ$, a distribution with compact support, this representation has the form $ ψ_t = E(Y_t(ψ))$ where the process $ (Y_t(ψ))$ is the solution of a stochastic partial differential equation connected with the stochastic differential equation for $ (X_t) $ via Ito's formula.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/0706.3352
dc.identifierhttp://arxiv.org/abs/0706.3352
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132279
dc.subjectProbability
dc.subjectAnalysis of PDEs
dc.titleProbabilistic Representations of Solutions of the Forward Equations
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