One-sided convergence of continuous processes of stochastic approximation

Komarov, S. V.; Krasulina, T. P.

doi:10.1007/bf02364822

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2023

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“…Having advanced tools of stochastic analysis at their disposal-in particular the Lyapunov functions method from the stability theory of stochastic differential equations-they showed that sufficient conditions on coefficients of (1) implying convergence of its solutions almost surely as t → ∞ to the (unique) root of the drift R may be found and proved in a straightforward and transparent way. See their book [21] for a systematic development of these ideas and, for example, the papers [6,11,22] and the book [12] for further results on continuous-time stochastic approximation.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Approximation Procedures for Lévy-Driven SDEs

Seidler

Týbl²

2023

J Optim Theory Appl

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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.

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