A second-order Stratonovich differential equation with boundary conditions

Aureli Alabert, David Nualart

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient σẊt and boundary conditions X0 = 0 and X1 = 1 is a 2-Markov field if and only if the drift is a linear function. The proof is based on the method of change of probability and makes use of the techniques of Malliavin calculus.
Original languageEnglish
Pages (from-to)21-47
JournalStochastic Processes and their Applications
Volume68
DOIs
Publication statusPublished - 30 May 1997

Keywords

  • Girsanov transformations
  • Markov fields
  • Non-causal stochastic calculus
  • Stochastic differential equations

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