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Ukrainian Mathematical Journal

, Volume 56, Issue 5, pp 774–789 | Cite as

On the solution of a one-dimensional stochastic differential equation with singular drift coefficient

  • A. M. Kulik
Article
  • 21 Downloads

Abstract

We determine generalized diffusion coefficients and describe the structure of local times for a process defined as a solution of a one-dimensional stochastic differential equation with singular drift coefficient.

Keywords

Differential Equation Diffusion Coefficient Local Time Stochastic Differential Equation Generalize Diffusion 
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.
    Harrison, J. M., Shepp, L. A. 1981On skew Brownian motionAnn. Probab.9309313Google Scholar
  2. 2.
    Nakao, S. 1972On the pathwise uniqueness of solutions of one-dimensional stochastic differential equationsOsaka J. Math.9513518Google Scholar
  3. 3.
    Portenko, N. I. 1986To the theory of the generalized diffusionProceedings of the Third Bad Honnef Conference “Stochastic Differential Systems” (June 3-7, 1985), Lect. Notes Control and Inf. Sci.78340341Google Scholar
  4. 4.
    Portenko, N. I. 1982Generalized Diffusion ProcessesNaukaKievin RussianGoogle Scholar
  5. 5.
    Gall, J.-F. 1984One-dimensional stochastic differential equations involving the local times of the unknown processStochastic Analysis and Applications (Swansea, 1983), Lect. Notes Math.10955182Google Scholar
  6. 6.
    Shevchenko, G. 2002On a generalized diffusion process with a drift that is the generalized derivative of a singular functionProceedings of the Ukrainian Mathematical Congress (Kiev, 2001)Institute of Mathematics, Ukrainian Academy of SciencesKiev139148Google Scholar
  7. 7.
    Engelbert, H. J., Schmidt, W. 1991Strong Markov continuous local martingales and solutions of one-dimensional stochastic differential equations. IIIMath. Nachr.151149151Google Scholar
  8. 8.
    Barlow, M., Perkins, E. 1984One-dimensional stochastic differential equations involving a singular increasing processStochastics12229249Google Scholar
  9. 9.
    F. Flandoli, F. Russo, and J. Wolf, Some Stochastic Differential Equations with Distributional Drift, Preprint No. 00-03-09, Bielefeld (2000).Google Scholar
  10. 10.
    Ikeda, N., Watanabe, S. 1981Stochastic Differential Equations and Diffusion ProcessesNorth-HollandAmsterdamGoogle Scholar
  11. 11.
    Weinrub, S. 1981Etude d’une equation differentielle stochastique avec temps localSemin. Probab.9867277Google Scholar
  12. 12.
    Gikhman, I. I., Skorokhod, A. V. 1982Stochastic Differential Equations and Their ApplicationsNaukova DumkaKievin RussianGoogle Scholar
  13. 13.
    Zaitseva, L. L. 2000On a probabilistic approach to the construction of the generalized diffusion processesTheor. Stochast. Process6141146Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • A. M. Kulik
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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