### Abstract

Consider the stochastic integral equation (S.I.E.) X(t) = H(t)+ ∫_{0+}^{t}f(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 H_{1} or H_{2} (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 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics