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Representation theorems for generators of backward stochastic differential equations and their applications. (English) Zbl 1078.60043
Summary: We prove that the generator $g$ of a backward stochastic differential equation (BSDE) can be represented by the solutions of the corresponding BSDEs at point $(t,y,z)$ if and only if $t$ is a conditional Lebesgue point of generator $g$ with parameters $(y,z)$. By this conclusion, we prove that, if $g$ is a Lebesgue generator and $g$ is independent of $y$, then Jensen’s inequality for $g$-expectation holds if and only if $g$ is super homogeneous; we also obtain a converse comparison theorem for deterministic generators of BSDEs.

MSC:
 60H10 Stochastic ordinary differential equations
Full Text:
References:
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