BACKWARD SDEs AND SOBOLEV SOLUTIONS FOR SEMILINEAR PARABOLIC PDEs WITH SINGULAR COEFFICIENTS

2011 ◽  
Vol 14 (03) ◽  
pp. 517-536 ◽  
Author(s):  
TUSHENG ZHANG ◽  
QIKANG RAN
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Parabolic Pdes ◽  
Singular Coefficients ◽  
Semilinear Parabolic ◽  
Backward Sdes

In this paper, we construct the solutions of semilinear parabolic PDEs with singular coefficients and establish the link to solutions of backward stochastic differential equations.

scholarly journals Anticipated backward SDEs with jumps and quadratic-exponential growth drivers

2019 ◽  
Vol 19 (03) ◽  
pp. 1950020
Author(s):  
Masaaki Fujii ◽  
Akihiko Takahashi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Unique Solution ◽  
Exponential Growth ◽  
Linear Growth ◽  
Uniform Norm ◽  
Backward Stochastic Differential Equations ◽  
Forward Process ◽  
Backward Sdes

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple [Formula: see text] where [Formula: see text] is a semimartingale, and [Formula: see text] are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of [Formula: see text]’s future paths, as well as quadratic and exponential growth on the spot values of [Formula: see text], respectively. The existence of the unique solution is proved for Markovian and non-Markovian settings with different structural assumptions on the driver. In the former case, some regularities on [Formula: see text] with respect to the forward process are also obtained.

Sign in / Sign up

Export Citation Format

Share Document