| 宋阳.单调性条件下G-Brown运动驱动的倒向随机微分方程[J].数学年刊A辑,2019,40(2):177~198 |
| 单调性条件下G-Brown运动驱动的倒向随机微分方程 |
| Backward Stochastic Differential Equations Driven by G-Brownian Motion Under a Monotonicity Condition |
| Received:October 19, 2016 Revised:July 14, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0015 |
| 中文关键词: G-Brownian motion, Backward SDEs, Monotonicity condition |
| 英文关键词:G-Brownian motion, Backward SDEs, Monotonicity condition |
| 基金项目: |
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| 中文摘要: |
| 研究了由$G${-}Brown运动驱动的倒向随机微分方程
\begin{align*}
Y_{t}=\xi+\int_{t}^{T}f(s, Y_{s}, Z_{s})\rmd s-\int_{t}^{T}Z_{s}\rmd B_{s}-(K_{T}-K_{t}), \quad 0\leq t \leq T
\end{align*}
解的存在唯一性问题.其生成元$f$关于$z$是Lipschitz连续的, 关于$y$是线性增长且满足单调性条件. |
| 英文摘要: |
| In this paper, the solution of backward stochastic differential equations
driven by a $G${-}Brownian motion ($G$-BSDE for short):
$$
Y_{t}=\xi+\int_{t}^{T}f(s, Y_{s}, Z_{s})\rmd s-\int_{t}^{T}Z_{s}\rmd B_{s}-(K_{T}-K_{t}), \quad0\leq t\leq T
$$
is studied, with a generator which is Lipschitz in $Z$, uniformly
continuous with linear growth and satisfying a monotonicity condition
in $Y$. |
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