A diffusion approximation result for two parameter processes

Rene A. Carmona, Jean Pierre Fouque

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We consider a one-dimensional linear wave equation with a small mean zero dissipative field and with the boundary condition imposed by the so-called Goursat problem. In order to observe the effect of the randomness on the solution we perform a space-time rescaling and we rewrite the problem in a diffusion approximation form for two parameter processes. We prove that the solution converges in distribution toward the solution of a two-parameter stochastic differential equation which we identify. The diffusion approximation results for oneparameter processes are well known and well understood. In fact, the solution of the one-parameter analog of the problem we consider here is immediate. Unfortunately, the situation is much more complicated for two-parameter processes and we believe that our result is the first one of its kind.

Original languageEnglish (US)
Pages (from-to)277-298
Number of pages22
JournalProbability Theory and Related Fields
Volume98
Issue number3
DOIs
StatePublished - Sep 1 1994
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'A diffusion approximation result for two parameter processes'. Together they form a unique fingerprint.

  • Cite this