Long time behavior of diffusions with Markov switching

By Jean-Baptiste Bardet, H. Guerin, Florent Malrieu. 2009

67 citations recorded by the source corpus.

Let $Y$ be an Ornstein-Uhlenbeck diffusion governed by an ergodic finite state Markov process $X$: $dY_t=-\lambda(X_t)Y_tdt+\sigma(X_t)dB_t$, $Y_0$ given. Under ergodicity condition, we get quantitative estimates for the long time behavior of $Y$. We also establish a trichotomy for the tail of the stationary distribution of $Y$: it can be heavy (only some moments are finite), exponential-like (only some exponential moments are finite) or Gaussian-like (its Laplace transform is bounded below and above by Gaussian ones). The critical moments are characterized by the parameters of the model.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f8b4ebb5641c08817a7c60b39267ae9d06899a88

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Quantitative ergodicity for some switched dynamical systems (2012, background): “Many results are available both in the discrete time setting (see [26, 33, 21, 25, 1]) and in the continuous time setting (see [24, 16, 4]).”