On one-dimensional stochastic differential equations driven by stable processes
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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.
Keywordssymmetric α-stable Lévy process stable integral stochastic differential equation weak nonexploding solution Skorokhod representation theorem L2-estimate
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