Lithuanian Mathematical Journal

, Volume 40, Issue 3, pp 277–295 | Cite as

On one-dimensional stochastic differential equations driven by stable processes

  • H. Pragarauskas
  • P. A. Zanzotto
Article

Abstract

We consider the one-dimensional stochastic differential equation dXt=b(t, Xt−) dZt, whereZ is a symmetric α-stable Lévy process with α ε (1, 2] andb is a Borel function. We give sufficient conditions under which the equation has a weak nonexploding solution.

Keywords

symmetric α-stable Lévy process stable integral stochastic differential equation weak nonexploding solution Skorokhod representation theorem L2-estimate 

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Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • H. Pragarauskas
    • 1
  • P. A. Zanzotto
    • 2
  1. 1.Institute of Mathematics and InformaticsVilniusLithuania
  2. 2.Department of MathematicsUniversity of PisaPisaItaly

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