On one-dimensional stochastic differential equations driven by stable processes
Copyright policy )On one-dimensional stochastic differential equations driven by stable processes
It is considered the one-dimensional stochastic differential equation \[ X_t= x+ \int^t_0 b(s, X_{s-}) dZ_s,\qquad t\geq 0,\tag{\(*\)} \] where \(Z\) is a symmetry \(\alpha\)-stable Lévy process with \(\alpha\in (1,2]\) and \(b\) is a Borel function. If for all \(t>0\) and \(R> 0\) \[ \int^t_0 \int^R_{-R} (|b(s,y)|^\alpha+|b(s,y)|^{-\alpha}) ds dy 0, \] where \(\lambda\) denotes the Lebesgue measure, it is proved that for every \(x\in R^1\) there exists a weak nonexploding solution to \((*)\).
- University of Pisa Italy
- University of Udine Italy
Stable stochastic processes, weak solution, stochastic differential equation, Stochastic ordinary differential equations (aspects of stochastic analysis), \(\alpha\)-stable Lévy process
Stable stochastic processes, weak solution, stochastic differential equation, Stochastic ordinary differential equations (aspects of stochastic analysis), \(\alpha\)-stable Lévy process
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