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Multivalued backward stochastic differential equations with time delayed generators

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Diomande B., Maticiuc L.

Open Mathematics

2014

tom 12

nr 11

1624-1637

Our aim is to study the following new type of multivalued backward stochastic differential equation: $$\left\{ \begin{gathered} - dY\left( t \right) + \partial \phi \left( {Y\left( t \right)} \right)dt \ni F\left( {t,Y\left( t \right),Z\left( t \right),Y_t ,Z_t } \right)dt + Z\left( t \right)dW\left( t \right), 0 \leqslant t \leqslant T, \hfill \\ Y\left( T \right) = \xi , \hfill \\ \end{gathered} \right.$$ 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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1 Open Mathematics

1 Diomande B.

1 Maticiuc L.

1 2014

Wyniki wyszukiwania

Multivalued backward stochastic differential equations with time delayed generators