On one-dimensional stochastic differential equations driven by stable processes |
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| Authors: | H Pragarauskas P A Zanzotto |
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| Institution: | (1) Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania;(2) Department of Mathematics, University of Pisa, Via F. Buonarroti 2, 56127 Pisa, Italy |
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| Abstract: | We consider the one-dimensional stochastic differential equation dX
t=b(t, Xt−) dZ
t, 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.
Partially supported by Programma Professori Visitatori of G. N. A. F. A. (Italy).
Partially supported by MURST (Italy). The present research was completed while the second author was visiting the Institute
of Mathematics and Informatics (Vilnius, Lithuania) in spring of 1999.
Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 361–385, July–September, 2000.
Translated by H. Pragarauskas |
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| Keywords: | symmetric α -stable Lévy process stable integral stochastic differential equation weak nonexploding solution Skorokhod representation theorem L 2-estimate |
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