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Stochastic equations with discontinuous jump functions

Abstract

In the present article, we consider a stochastic differential equation that contains an integral with respect to a Poisson measure but avoids the diffusion term. The integrand need not be continuous. We introduce a definition of a solution and prove the existence and uniqueness theorems.

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Correspondence to A. V. Logachov.

Additional information

Original Russian Text © A. V. Logachov and S. Ya. Makhno, 2017, published in Matematicheskie Trudy, 2017, Vol. 20, No. 1, pp. 128–144.

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Logachov, A.V., Makhno, S.Y. Stochastic equations with discontinuous jump functions. Sib. Adv. Math. 27, 263–273 (2017). https://doi.org/10.3103/S1055134417040046

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Keywords

  • stochastic differential equation
  • Poisson measure
  • differential inclusions