A diffusion approximation result for two parameter processes

René A. Carmona, Jean Pierre Fouque

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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
Issue number3
StatePublished - Sep 1994
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Mathematics Subject Classifications (1991): 60H15


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