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Multivalued backward stochastic differential equations with time delayed generators

Bakarime DiomandeLucian Maticiuc — 2014

Open Mathematics

Our aim is to study the following new type of multivalued backward stochastic differential equation: - d Y t + φ Y t d t F t , Y t , Z t , Y t , Z t d t + Z t d W t , 0 t T , Y T = ξ , where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.

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