无界停时终端非李氏系数带跳倒向随机微分方程的解及拟线性椭圆型偏微分积分方程解的概率表示

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基金项目: 国家自然科学基金资助项目(79790130);中山大学前沿项目基金

On Solutions of Backward Stochastic Differential Equations With Jumps,With Unbounded Stopping Times as Terminal and With Non-Lipschitz Coefficients,and Probabilistic Interpretationof Quasi-Linear Elliptic TypeIntegro-Differential Equations

摘要: 对终端为无界停时的带跳倒向随机微分方程,在非李氏条件下证得了解的存在唯一性.推导出这类方程解的若干收敛定理与解对参数的连续依赖性,还得到了关于拟线性随圆型偏微分积分方程解的概率表示.
- 带跳倒向随机微分方程 /
- 无界停时 /
- 适应解 /
- 解的收敛性 /
- 拟线性椭圆型方程 /
- 偏微分积分算子
Abstract: The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non-Lipschitz condition are obtained.The convergence of solutions and the continuous dependence of solutions on parameters are also derived.Then the probabilistic interpretation of solutions to some kinds of quasi-linear elliptic type integrodifferential equations is obtained.
- backward stochastic differential equations(BSDEs) with jumps /
- unbounded stopping time /
- adapted solutions /
- convergence of solutions /
- quasi-linear elliptic equations /
- integro-defferential operators.

[1]	El Karoui N,Peng S,Quenez M C.Backward stochastic differential equations in finance[J].Math F in ance,1997,7(1):1~71.
[2]	Peng S.Probabilistic interpretation for system of quasi-linear parabolic partial differential equations[J].Stochastics and Stochastics Reports,1991,37:61~74.
[3]	Peng S.Backward stochastic differential equations[A].In:Lecture Notes on Stocha stic Calculus and Applications to Mathematical Finance[C].Beijing:CIMPA School,1994.
[4]	Situ Rong.On solutions of backward stochastic differential equations with jumps and applications[J].Stochastic Process Appl,1997,66(2):209~236.
[5]	Darling R,Pardoux E.Backward SDE with random time and applications to semi-linear elliptic PDE[J].Anna Prob,1997,25(3):1135~1159.
[6]	陈增敬.带有停时的倒向随机微分方程解的存在性[J].科学通报,1997,42(22):2379~2382.
[7]	Tang S,Li X.Necessary conditions for optimal control of stochastic system with random jumps[J].SIAM J Control Optim,1994,32(5):1447~1475.
[8]	Ladyzenskaja O,Uralceva N N.Linear and Qua silinear Elliptic Equations[M].N Y:Academic Press,1968.
[9]	Situ Rong.On strong solutions,uniqueness,stability and comparison theorem for a stochastic system with Poisson jumps[A].In:Lecture Notes in Control and Inform Sci[C].Berlin-New York:Springer,1985,75:352~381.