Journal
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volume 115, Issue 12, Pages 1883-1903Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.spa.2005.06.008
Keywords
backward stochastic differential equation; representation theorem; conditional Lebesgue point; Lebesgue generator; g-expectation; converse comparison theorem
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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. (c) 2005 Elsevier B.V. All rights reserved.
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