Stochastic Approximation Procedures for Lévy-Driven SDEs

Jan Seidler () and Ondřej Týbl ()
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Jan Seidler: Institute of Information Theory and Automation
Ondřej Týbl: Faculty of Mathematics and Physics

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 2, No 15, 817-837

Abstract: 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.

Keywords: Stochastic approximation algorithms; Robbins–Monro procedure; Lévy-driven stochastic differential equations; 60H10; 62L20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02198-0

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