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Ukrainian Mathematical Journal

, Volume 49, Issue 6, pp 966–975 | Cite as

On the existence and uniqueness of a solution of a linear stochastic differential equation with respect to a logarithmic process

  • A. Yu. Pilipenko
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Abstract

We study the problem of existence and uniqueness of a solution of a linear stochastic differential equation with respect to a logarithmic process. For the conditional mathematical expectation of a solution, we obtain a partial differential equation.

Keywords

Wiener Process Logarithmic Derivative Wiener Measure Stochastic Differential Equa Linear Stochastic Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    V. I. Averbukh, O. G. Smolyanov, and S. V. Fomin, “Generalized functions and differential equations in linear spaces. I. Differentiable measures,” Tr. Mosk. Mat. Obshch., No. 24, 133–174 (1971).zbMATHGoogle Scholar
  2. 2.
    A. A. Dorogovtsev, Stochastic Equations with Anticipation [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1996).Google Scholar
  3. 3.
    O. M. Kulyk, Random Operators and Stochastic Integral Equations [in Ukrainian], Author’s Abstract of the Candidate Degree Thesis (Physics and Mathematics), Kiev (1996).Google Scholar
  4. 4.
    R. Buckdahn, “Anticipative Girsanov transformations and Skorokhod stochastic differential equations,” Mem. Am. Math. Soc., 111, No. 533, 1–88 (1994).MathSciNetGoogle Scholar
  5. 5.
    A. Yu. Pilipenko, “Conditional analysis in non-Gaussian stochastic calculus, “Theory Rand Processes (to appear)Google Scholar
  6. 6.
    R. Courant, Partial Differential Equations, New York-London (1962).Google Scholar
  7. 7.
    S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics [in Russian], Nauka, Moscow (1988).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A. Yu. Pilipenko

There are no affiliations available

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