Probabilistic Representations of Solutions of the Forward Equations View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2008-03

AUTHORS

B. Rajeev, S. Thangavelu

ABSTRACT

In this paper we prove a stochastic representation for solutions of the evolution equation where L ∗ is the formal adjoint of a second order elliptic differential operator L, with smooth coefficients, corresponding to the infinitesimal generator of a finite dimensional diffusion (Xt). Given ψ0 = ψ, a distribution with compact support, this representation has the form ψt = E(Yt(ψ)) where the process (Yt(ψ)) is the solution of a stochastic partial differential equation connected with the stochastic differential equation for (Xt) via Ito’s formula. More... »

PAGES

139-162

References to SciGraph publications

  • 2003-08. Probabilistic representations of solutions to the heat equation in PROCEEDINGS - MATHEMATICAL SCIENCES
  • 1965. Markov Processes, Volume 1 in NONE
  • 2001. From Tanaka’s Formula to Ito’s Formula: Distributions, Tensor Products and Local Times in SÉMINAIRE DE PROBABILITÉS XXXV
  • 1981-07. Stochastic evolution equations in JOURNAL OF SOVIET MATHEMATICS
  • 1982. Mecanique aleatoire in ECOLE D'ETÉ DE PROBABILITÉS DE SAINT-FLOUR X - 1980
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11118-007-9074-0

    DOI

    http://dx.doi.org/10.1007/s11118-007-9074-0

    DIMENSIONS

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