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W-symmetries of jump-diffusion Itô stochastic differential equations

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Abstract

In this article, we discuss Lie point symmetry of stochastic differential equations driven by Wiener and Poisson processes. The symmetry is obtained by considering infinitesimals involving not only spatial and temporal variables but also that of vector Wiener process variable W(t). This work leads to the derivation of the random time-change formula of Itô Brownian motion in Lie transformation context.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch, 7701, South Africa

    Aminu M. Nass & E. Fredericks

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  1. Aminu M. Nass
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  2. E. Fredericks
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Correspondence to Aminu M. Nass.

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Nass, A.M., Fredericks, E. W-symmetries of jump-diffusion Itô stochastic differential equations. Nonlinear Dyn 90, 2869–2877 (2017). https://doi.org/10.1007/s11071-017-3848-8

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  • DOI: https://doi.org/10.1007/s11071-017-3848-8

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