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Stochastic invariant imbedding
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  • Published: June 1995

Stochastic invariant imbedding

Application to stochastic differential equations with boundary conditions

  • J. Garnier1 

Probability Theory and Related Fields volume 103, pages 249–271 (1995)Cite this article

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  • 4 Citations

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Summary

We study stochastic differential equations of the type:

$$dx_t = f(t,x_t )dt + \sum\limits_{k = 1}^d {\sigma ^k (t,x_t )} \bigcirc dw_t^k ,x \in \mathbb{R}^d ,t \in [0,T_0 ].$$

Instead of the customary initial value problem, where the initial valuex 0 is fixed, we impose an affine boundary condition:

$$h_0 x_0 + h_1 x_{T_0 } = \upsilon _0 ,$$

whereh 0,h 1 are deterministic matrices andv 0 is a fixed vector. Our main aim is to prove existence and uniqueness results for such anticipating stochastic differential equations.

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Authors and Affiliations

  1. Centre de Mathématiques Appliquées, Ecole Polytechnique, F-91128, Palaiseau Cedex, France

    J. Garnier

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  1. J. Garnier
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Cite this article

Garnier, J. Stochastic invariant imbedding. Probab. Th. Rel. Fields 103, 249–271 (1995). https://doi.org/10.1007/BF01204217

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  • Received: 21 September 1994

  • Revised: 14 February 1995

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01204217

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Mathematics Subject Classification (1991)

  • 34K10
  • 60H10
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