Central European Journal of Mathematics

, Volume 12, Issue 11, pp 1624–1637 | Cite as

Multivalued backward stochastic differential equations with time delayed generators

Research Article

Abstract

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 (Yt, Zt):= (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.

Keywords

Backward stochastic differential equations Time-delayed generators Subdifferential operator 

MSC

60H10 47J20 49J40 

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Copyright information

© Versita Warsaw and Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.Faculty of Mathematics“Alexandru Ioan Cuza” UniversityIaşiRomania
  2. 2.Department of Mathematics“Gheorghe Asachi” Technical UniversityIaşiRomania

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