Hyperbolic stochastic differential equations: Absolute continuity of the law of the solution at a fixed point

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Abstract

Let W be the Wiener process on T = [0, 1]2. Consider the stochastic integral equation (Equation Presented) where Rζ = {(s′, t′) ∈ T: s′ ≤ s, t′ ≤ t}, ζ = (s, t) ∈ T, and x0 ∈ ℝ. Under some assumptions on the coefficients ai, the existence and uniqueness of a solution for this stochastic integral equation is already known (see [6]). In this paper we present some sufficient conditions for the law of Xζ to have a density. © 1996 Springer-Verlag New York Inc.
Original languageEnglish
Pages (from-to)293-313
JournalApplied Mathematics and Optimization
Volume33
Issue number3
Publication statusPublished - 1 Dec 1996

Keywords

  • Hyperbolic stochastic partial differential equations
  • Malliavin calculus
  • Two-parameter representable semimartingales

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