Nonlinear stochastic integral equations in the plane

M. Farré, D. Nualart

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

Let W = {Wζ, ζ ε{lunate} T} be the two-parameter Wiener process on T = [0, 1]2. Consider the nonlinear stochastic partial differential equation: ∂2Xs, t ∂s ∂t= a3(X, s, t) ∂W2s, t ∂s ∂t+a4(X, s, t)+a1(s, t) ∂Xs, t ∂s+a2(s, t) ∂Xs, t ∂t. We give a rigorous meaning to the notion of solution for this equation, by rewriting it as an integral equation which involves a stochastic integral term and mixed-line integrals with respect to the representable semimartingale X. Under some assumptions on the coefficients a1, we prove the existence and uniqueness of solution for this stochastic integral equation. © 1993.
Original languageEnglish
Pages (from-to)219-239
JournalStochastic Processes and their Applications
Volume46
DOIs
Publication statusPublished - 1 Jan 1993

Keywords

  • hyperbolic stochastic partial differential equations
  • representable semimartingales
  • two-parameter Wiener process

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