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Stratonovich covariant differential equation with jumps

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  • Maillard-Teyssier, Laurence

Abstract

We study Stratonovich s.d.e. driven by semimartingales in the tangent bundle over a differentiable manifold M. In ordinary differential geometry, a connection on M is needed to define the covariant derivative of a C1 curve in ; by the transfer principle, Elworthy and Norris have defined a Stratonovich covariant integration along a continuous semimartingale in . We extend this to the case when the semimartingale jumps, using Norris's work and Cohen's results on s.d.e. with jumps on manifolds, in order to give a discretization theorem for such Stratonovich covariant s.d.e. with jumps.

Suggested Citation

  • Maillard-Teyssier, Laurence, 2006. "Stratonovich covariant differential equation with jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1860-1875, December.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:12:p:1860-1875
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    Cited by:

    1. Mirzaee, Farshid & Hadadiyan, Elham, 2017. "Solving system of linear Stratonovich Volterra integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 254-264.

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