Nonlinear stochastic integral equations in the plane

M. Farré and D. Nualart

Stochastic Processes and their Applications, 1993, vol. 46, issue 2, 219-239

Abstract: Let W = {W[zeta], [zeta] [epsilon] T} be the two-parameter Wiener process on T = [0, 1]2. Consider the nonlinear stochastic partial differential equation: . 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.

Keywords: hyperbolic; stochastic; partial; differential; equations; two-parameter; Wiener; process; representable; semimartingales (search for similar items in EconPapers)
Date: 1993
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