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Stochastic Approximation Procedures for Lévy-Driven SDEs

Author

Listed:
  • Jan Seidler

    (Institute of Information Theory and Automation)

  • Ondřej Týbl

    (Faculty of Mathematics and Physics)

Abstract

We consider a continuous-time Robbins–Monro-type stochastic approximation procedure for a system described by a (multidimensional) stochastic differential equation driven by a general Lévy process, and we find sufficient conditions for its convergence in terms of Lyapunov functions. While the jump part of the noise may spoil convergence to the root of the drift in some cases, we show that by a suitable choice of noise coefficients we obtain convergence under hypotheses on the drift weaker than those used in the diffusion case or convergence to a selected root in the case of multiple roots of the drift.

Suggested Citation

  • Jan Seidler & Ondřej Týbl, 2023. "Stochastic Approximation Procedures for Lévy-Driven SDEs," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 817-837, May.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:2:d:10.1007_s10957-023-02198-0
    DOI: 10.1007/s10957-023-02198-0
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