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On solutions of stochastic differential equations with drift
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  • Published: September 1990

On solutions of stochastic differential equations with drift

  • M. Rutkowski1 

Probability Theory and Related Fields volume 85, pages 387–402 (1990)Cite this article

Summary

We study stochastic differential equations of the formdX t=σ(X t)dMt+b(Xt)d<M>t whereM is a continuous local martingale and <M> stands for its quadratic variation process. The conditions introduced by Engelbert and Schmidt, which ensure the existence and uniqueness in law of solutions of SDE's driven by the Wiener process without drift (or with generalized drift) are shown to be no longer valid.

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Authors and Affiliations

  1. Institute of Mathematics, Politechnika Warszawska, Pl. Jedności Robotniczej 1, 00-661, Warszawa, Poland

    M. Rutkowski

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  1. M. Rutkowski
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Rutkowski, M. On solutions of stochastic differential equations with drift. Probab. Th. Rel. Fields 85, 387–402 (1990). https://doi.org/10.1007/BF01193944

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  • Received: 17 November 1988

  • Revised: 08 August 1989

  • Issue Date: September 1990

  • DOI: https://doi.org/10.1007/BF01193944

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Keywords

  • Differential Equation
  • Stochastic Process
  • Probability Theory
  • Variation Process
  • Mathematical Biology
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