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 |
|---|---|
| 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
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On the stochastic integral equations with non-Lipschitz coefficients. / Cheng, Tsung Lin.
In: Stochastic Analysis and Applications, Vol. 20, No. 2, 01.01.2002, p. 283-298.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 -