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On solutions of one-dimensional stochastic differential equations driven by stable Lévy motion

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  • Zanzotto, P. A.

Abstract

We consider the stochastic differential equation dXt= b(Xt)dZt, t[greater-or-equal, slanted]o, where b is a Borel measurable real function and Z is a symmetric [alpha]-stable Lévy motion. In Section 1 we study the convergence of certain functionals of Z and in particular, we extend Engelbert and Schmidt 0-1 law (for functionals of the Wiener process) to functionals of a symmetric [alpha]-stable Lévy motion with 1

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  • Zanzotto, P. A., 1997. "On solutions of one-dimensional stochastic differential equations driven by stable Lévy motion," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 209-228, June.
    • Handle: RePEc:eee:spapps:v:68:y:1997:i:2:p:209-228
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    References listed on IDEAS

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    1. Kallenberg, Olav, 1992. "Some time change representations of stable integrals, via predictable transformations of local martingales," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 199-223, March.
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    Cited by:

    1. Liu, He & Song, Wanqing & Li, Ming & Kudreyko, Aleksey & Zio, Enrico, 2020. "Fractional Lévy stable motion: Finite difference iterative forecasting model," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).

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