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A class of stochastic differential equations with pathwise unique solutions

Author

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  • B. Rajeev

    (Indian Statistical Institute)

  • K. Suresh Kumar

    (Indian Institute of Technology)

Abstract

We propose a new method viz., using stochastic partial differential equations to study the pathwise uniqueness of stochastic (ordinary) differential equations. We prove the existence and pathwise uniqueness of a class of stochastic differential equations with coefficients in suitable Hermite-Sobolev class using our approach.

Suggested Citation

  • B. Rajeev & K. Suresh Kumar, 2016. "A class of stochastic differential equations with pathwise unique solutions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(2), pages 343-355, June.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:2:d:10.1007_s13226-016-0191-6
    DOI: 10.1007/s13226-016-0191-6
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    References listed on IDEAS

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    1. B. Rajeev, 2013. "Translation invariant diffusions in the space of tempered distributions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(2), pages 231-258, April.
    2. Swart, J. M., 2002. "Pathwise uniqueness for a SDE with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 131-149, March.
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    Cited by:

    1. K. T. Joseph & K. Sandeep, 2019. "Theoretical developments in the study of partial differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(3), pages 681-704, September.

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