Abstract.
In this paper we study the path regularity of the adpated solutions to a class of backward stochastic differential equations (BSDE, for short) whose terminal values are allowed to be functionals of a forward diffusion. Using the new representation formula for the adapted solutions established in our previous work [7], we are able to show, under the mimimum Lipschitz conditions on the coefficients, that for a fairly large class of BSDEs whose terminal values are functionals that are either Lipschitz under the L ∞-norm or under the L 1-norm, then there exists a version of the adapted solution pair that has at least càdlàg paths. In particular, in the latter case the version can be chosen so that the paths are in fact continuous.
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Received: 26 May 2000 / Revised version: 1 December 2000 / Published online: 19 December 2001
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Ma, J., Zhang, J. Path regularity for solutions of backward stochastic differential equations. Probab Theory Relat Fields 122, 163–190 (2002). https://doi.org/10.1007/s004400100144
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DOI: https://doi.org/10.1007/s004400100144