On the Feynman-KAC's Formula and Its Applications to Filtering Theory.

Abstract

Let (x(t)) be a Markov process, not assumed to be time homogenous. It is well known that (s(t)bar) = (t, X(t)) is a time homogeneous Markov process. Let A be its generator. The Feynman-Kac's formula for x(t) takes the following form if the equation: (1,1) Av + cv = 0 admits a solution v, then v has the representation, for s < t: (1.2) v(s,Xs) = E v(t,Xt) exp(integral(stat) c(u,Xu)du) sigma(Xs). We prove this under general conditions on (Xt) .

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1986
Accession Number
ADA186014

Entities

People

  • Rajeeva L. Karandikar

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Equations
  • Filtration
  • Generators
  • Markov Processes
  • North Carolina
  • Probability
  • Scientific Research
  • Stochastic Processes
  • Transitions
  • Universities
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Data Mining and Knowledge Discovery.
  • Linear Algebra