On the stochastic integral equations with non-Lipschitz coefficients

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Abstract

Consider the stochastic integral equation (S.I.E.) X(t) = H(t)+ ∫0+tf(X(s-))dZs, t ∈ R+ (0.1) where f satisfies some non-Lipschitz condition and H,Z are ℱt- semimartingales, continuous or discontinuous, on some probability space (Ω, ℱ,{ℱt}t∈R+,P). We prove that if f satisfies Condition H1 or H2 (defined in Sec. 0), then both the existence and the uniqueness of the solutions of (0.1) hold.

Original languageEnglish
Pages (from-to)283-298
Number of pages16
JournalStochastic Analysis and Applications
Volume20
Issue number2
DOIs
Publication statusPublished - 2002 Jan 1

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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