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

By Alexey M.Kulik. 2007

72 citations recorded by the source corpus.

. 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 R 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 R m .

Subfields: Control and Systems Engineering, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e1dcca2eaf78be876a3bdec27d30c6c54bd3099c

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Citations in the corpus

Ergodicity of stochastic differential equations with jumps and singular coefficients (2017, background): “In [29] and [30], they introduced some abstract conditions for the ergodicity.”
Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency (2013, methodology): “If c is constant, then we can apply Kulik [19], Proposition 0.”
Exponential ergodicity and regularity for equations with Lévy noise (2011, background): “The paper [15] studied the exponential mixing of finite-dimensional stochastic systems with jump noises, which include one-dimensional SDEs driven by α-stable noise.”