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Exponential ergodicity of the solutions to SDE's with a jump noise

Alexei KulikORCID

Анотація

The mild sufficient conditions for exponential ergodicity of a Markov process, defined as the solution to SDE with a jump noise, are given. These conditions include three principal claims: recurrence condition R, topological irreducibility condition S and non-degeneracy condition N, the latter formulated in the terms of a certain random subspace of \Re^m, associated with the initial equation. The examples are given, showing that, in general, none of three principal claims can be removed without losing ergodicity of the process. The key point in the approach, developed in the paper, is that the local Doeblin condition can be derived from N and S via the stratification method and criterium for the convergence in variations of the family of induced measures on \Re^m.

Класифікація

Домен
Social SciencesPhysical Sciences
Галузь
Economics, Econometrics and FinanceDecision SciencesEngineering
Підгалузь
FinanceStatistics, Probability and UncertaintyControl and Systems Engineering
Тема
★Stochastic processes and financial applicationsProbabilistic and Robust Engineering DesignStability and Controllability of Differential Equations

Ідентифікатори

DOI: 10.48550/arxiv.math/0701747

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