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Supports for degenerate stochastic differential equations with jumps and applications

Author

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  • Qiao, Huijie
  • Wu, Jiang-Lun

Abstract

In the paper, we are concerned with degenerate stochastic differential equations with jumps. We first establish two theorems about supports for the solution laws of the degenerate stochastic differential equations, under different (sufficient) conditions. We then apply one of our results to a class of degenerate stochastic evolution equations (that is, stochastic differential equations in infinite dimensions) with jumps to obtain a characterisation of path-independence for the densities of their Girsanov transformations.

Suggested Citation

  • Qiao, Huijie & Wu, Jiang-Lun, 2021. "Supports for degenerate stochastic differential equations with jumps and applications," Statistics & Probability Letters, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:stapro:v:177:y:2021:i:c:s0167715221001383
    DOI: 10.1016/j.spl.2021.109176
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    References listed on IDEAS

    as
    1. Wu, Bo & Wu, Jiang-Lun, 2018. "Characterising the path-independent property of the Girsanov density for degenerated stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 71-79.
    2. Simon, Thomas, 2000. "Support theorem for jump processes," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 1-30, September.
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