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| The Cocycle Property of Stochastic Differential EquationsDriven by G-Brownian Motion |
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Citation： |
Huijie QIAO.The Cocycle Property of Stochastic Differential EquationsDriven by G-Brownian Motion[J].Chinese Annals of Mathematics B,2015,36(1):147~160 |
| Page view： 1551
Net amount： 1404 |
Authors： |
Huijie QIAO; |
Foundation： |
the National Natural Science Foundation of China (No. 11001051). |
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| Abstract： |
In this paper, solutions of the following non-Lipschitz stochastic
differential equations driven by G-Brownian motion:
\begin{align*}
X_t=x+\int_0^tb(s,\omega,X_s)\dif
s+\int_0^th(s,\omega,X_s)\dif\langle B\rangle _s
+\int_0^t\sigma(s,\omega,X_s)\dif B_s
\end{align*}
are constructed. It is shown that they have the cocycle property.
Moreover, under some special non-Lipschitz conditions, they are
bi-continuous with respect to $t,\,x$. |
Keywords： |
Cocycle property, Non-Lipschitz condition, SDEs driven by G-Brownian
motion |
Classification： |
60H05, 60H10, 60J65 |
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