On the stochastic integral equations with non-Lipschitz coefficients

Tsung Lin Cheng

doi:10.1081/SAP-120003435

On the stochastic integral equations with non-Lipschitz coefficients

Tsung Lin Cheng

Graduate Institute of Statistics and Information Science

Research output: Contribution to journal › Article › peer-review

Abstract

Consider the stochastic integral equation (S.I.E.) X(t) = H(t)+ ∫₀₊^tf(X(s^-))dZ_s, t ∈ R₊ (0.1) where f satisfies some non-Lipschitz condition and H,Z are ℱ_t- semimartingales, continuous or discontinuous, on some probability space (Ω, ℱ,{ℱ_t}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 language	English
Pages (from-to)	283-298
Number of pages	16
Journal	Stochastic Analysis and Applications
Volume	20
Issue number	2
DOIs	https://doi.org/10.1081/SAP-120003435
Publication status	Published - 2002 Jan 1

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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AB - 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.

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