### 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

### Cite this

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*Stochastic Analysis and Applications*, vol. 20, no. 2, pp. 283-298. https://doi.org/10.1081/SAP-120003435

**On the stochastic integral equations with non-Lipschitz coefficients.** / Cheng, Tsung Lin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the stochastic integral equations with non-Lipschitz coefficients

AU - Cheng, Tsung Lin

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0036016349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036016349&partnerID=8YFLogxK

U2 - 10.1081/SAP-120003435

DO - 10.1081/SAP-120003435

M3 - Article

AN - SCOPUS:0036016349

VL - 20

SP - 283

EP - 298

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

SN - 0736-2994

IS - 2

ER -