$L^p$ $(pgeq 1)$ solutions of multidimensional BSDEs with monotone generators in general time intervals


Abstract in English

In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equations in $L^p$ $(pgeq 1)$. We first study the existence and uniqueness for $L^p$ $(p>1)$ solutions by the method of convolution and weak convergence when the generator is monotonic in $y$ and Lipschitz continuous in $z$ both non-uniformly with respect to $t$. Then we obtain the existence and uniqueness for $L^1$ solutions with an additional assumption that the generator has a sublinear growth in $z$ non-uniformly with respect to $t$.

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