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Register a new userL^p -solution for BSDEs with jumps in the case p textless{} 2. Corrections to the paper BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration
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In [8] we established existence and uniqueness of solutions of backward stochastic differential equations in L^p under a monotonicity condition on the generator and in a general filtration. There was a mistake in the case 1 textless{} p textless{} 2. Here we give a corrected proof. Moreover the quasi-left continuity condition on the filtration is removed.
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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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