ﻻ يوجد ملخص باللغة العربية
This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of a scalar backward stochastic differential equation (BSDE) whose generator grows (with respect to both unknown variables $y$ and $z$) in a super-linear way like $|y||ln |y||^{(lambda+1/2)wedge 1}+|z||ln |z||^{lambda}$ for some $lambdageq 0$. For the following four different ranges of the growth power parameter $lambda$: $lambda=0$, $lambdain (0,1/2)$, $lambda=1/2$ and $lambda>1/2$, we give reasonably weakest possible different integrability conditions of the terminal value for the existence of an unbounded solution to the BSDE. In the first two cases, they are stronger than the $Lln L$-integrability and weaker than any $L^p$-integrability with $p>1$; in the third case, the integrability condition is just some $L^p$-integrability for $p>1$; and in the last case, the integrability condition is stronger than any $L^p$-integrability with $p>1$ and weaker than any $exp(L^epsilon)$-integrability with $epsilonin (0,1)$. We also establish the comparison theorem, which yields naturally the uniqueness, when either generator of both BSDEs is convex (concave) in both unknown variables $(y,z)$, or satisfies a one-sided Osgood condition in the first unknown variable $y$ and a uniform continuity condition in the second unknown variable $z$.
In this note, we prove that if $g$ is uniformly continuous in $z$, uniformly with respect to $(oo,t)$ and independent of $y$, the solution to the backward stochastic differential equation (BSDE) with generator $g$ is unique.
This paper is devoted to obtaining a wellposedness result for multidimensional BSDEs with possibly unbounded random time horizon and driven by a general martingale in a filtration only assumed to satisfy the usual hypotheses, i.e. the filtration may
We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial of degree
In this paper, we first study one-dimensional quadratic backward stochastic differential equations driven by $G$-Brownian motions ($G$-BSDEs) with unbounded terminal values. With the help of a $theta$-method of Briand and Hu [4] and nonlinear stochas
In [4], the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) if the terminal value is $Lexp{left(mu sqrt{2log{(1+L)}},right)}$-integrable with the positive parameter $mu$ being bigger