Lᵖ (p≥ 1) solutions of multidimensional BSDEs with monotone generators in general time intervals
Xiao, Lishun · Fan, Shengjun · Xu, Na
Original · EN
In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equations in Lᵖ (p≥ 1). We first study the existence and uniqueness for Lᵖ (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 L¹ solutions with an additional assumption that the generator has a sublinear growth in z non-uniformly with respect to t.
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