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An exploration of \(L^p\)-theory for forward-backward stochastic differential equations with random coefficients on small durations. (English) Zbl 1471.60092

Summary: In the present paper, under the Lipschitz condition and a monotonicity assumption, we obtain an \(L^p\)-result \((p>1)\), including the existence and uniqueness of the \(p\)-th power integrable solutions and a pair of related \(p\)-th power estimates, for coupled forward-backward stochastic differential equations with random coefficients on small durations. A measurable global implicit function theorem has been established and plays a key role in our analysis. It is the first measurable version of implicit function theorems to our best knowledge, therefore the theorems themselves have been improved.

MSC:

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