Advertisement

Ukrainian Mathematical Journal

, Volume 57, Issue 7, pp 1055–1065 | Cite as

On a Weak Solution of an Equation for an Evolution Flow with Interaction

  • M. P. Karlikova
Article

Abstract

We prove that a stochastic differential equation for an evolution flow with interaction whose coefficients do not satisfy the global Lipschitz condition has a weak solution.

Keywords

Differential Equation Weak Solution Stochastic Differential Equation Evolution Flow Lipschitz Condition 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    A. A. Dorogovtsev and P. Kotelenez, Stochastic Flows with Interaction and Random Measures, Kluwer, Dordrecht (2004).Google Scholar
  2. 2.
    R. M. Dudley, Real Analysis and Probability, Cambridge University Press, Cambridge (2002).Google Scholar
  3. 3.
    H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, Cambridge (1997).Google Scholar
  4. 4.
    P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • M. P. Karlikova
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

Personalised recommendations