Probability Theory and Related Fields. Manuscript-nr. Stochastic Invariant Imbedding Application to Stochastic Diierential Equations with Boundary Conditions

@inproceedings{Garnier1997ProbabilityTA,
  title={Probability Theory and Related Fields. Manuscript-nr. Stochastic Invariant Imbedding Application to Stochastic Diierential Equations with Boundary Conditions},
  author={J. Garnier},
  year={1997}
}
We study stochastic diierential equations of the type : dx t = f(t; x t)dt + d X k=1 k (t; x t) dw k t ; x 2 IR d ; t 2 0; T 0 ]: Instead of the customary initial value problem, where the initial value x 0 is xed, we impose an aane boundary condition : h 0 x 0 + h 1 x T0 = v 0 ; where h 0 , h 1 are deterministic matrices and v 0 is a xed vector. Our main aim is to prove existence and uniqueness results for such anticipating stochastic diierential equations. 

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