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Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions

Author

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  • Samorodnitsky, G.
  • Grigoriu, M.

Abstract

We describe the exact tail behavior of the solutions to certain nonlinear stochastic differential equations driven by Lévy motions with regularly varying tails and establish existence and uniqueness of solutions to these equations.

Suggested Citation

  • Samorodnitsky, G. & Grigoriu, M., 2003. "Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 69-97, May.
    • Handle: RePEc:eee:spapps:v:105:y:2003:i:1:p:69-97
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    Cited by:

    1. Jakubowski, Tomasz, 2007. "The estimates of the mean first exit time from a ball for the [alpha]-stable Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1540-1560, October.
    2. Dai Pra, P. & Pigato, P., 2015. "Multi-scaling of moments in stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3725-3747.
    3. Kulik, Alexei & Pavlyukevich, Ilya, 2021. "Moment bounds for dissipative semimartingales with heavy jumps," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 274-308.
    4. Imkeller, P. & Pavlyukevich, I., 2006. "First exit times of SDEs driven by stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 611-642, April.
    5. Li, Zenghu & Ma, Chunhua, 2015. "Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3196-3233.

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