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\(L^p\) solutions of anticipated BSDEs with weak monotonicity and general growth generators. (English) Zbl 07551423

Summary: In this article, we establish the stability theorems of \(L^p(1 < p \leq 2)\) solutions for multidimensional anticipated backward stochastic differential equations (BSDEs), in which the generator \(g\) is \(p\)-order weak monotonic in \(y\) and Lipschitz continuous in \((z, \eta, \vartheta)\). Moreover, we present the existence and uniqueness of \(L^p\) solutions for this kind of anticipated BSDEs with the help of stability theorems when generator \(g\) also satisfies general growth condition in \(y\).

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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