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

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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.

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References

  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).

    MATH  Google Scholar 

  2. A. A. Dorogovtsev, Stochastic Equations with Anticipation [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1996).

    Google Scholar 

  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).

  4. R. Buckdahn, “Anticipative Girsanov transformations and Skorokhod stochastic differential equations,” Mem. Am. Math. Soc., 111, No. 533, 1–88 (1994).

    MathSciNet  Google Scholar 

  5. A. Yu. Pilipenko, “Conditional analysis in non-Gaussian stochastic calculus, “Theory Rand Processes (to appear)

  6. R. Courant, Partial Differential Equations, New York-London (1962).

  7. S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics [in Russian], Nauka, Moscow (1988).

    Google Scholar 

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Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 6, pp. 863–871, June, 1997.

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Pilipenko, A.Y. On the existence and uniqueness of a solution of a linear stochastic differential equation with respect to a logarithmic process. Ukr Math J 49, 966–975 (1997). https://doi.org/10.1007/BF02513440

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  • DOI: https://doi.org/10.1007/BF02513440

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