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 language | English |
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Pages (from-to) | 283-298 |
Number of pages | 16 |
Journal | Stochastic Analysis and Applications |
Volume | 20 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2002 Jan 1 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics