6533b7d9fe1ef96bd126d675

RESEARCH PRODUCT

Quantitative ergodicity for some switched dynamical systems

Stéphane Le BorgnePierre-andré ZittFlorent MalrieuMichel Benaïm

subject

Statistics and ProbabilitySwitched dynamical systemsDynamical systems theoryMarkov process01 natural sciences34D2393E15010104 statistics & probabilitysymbols.namesakeCouplingPiecewise Deterministic Markov ProcessPosition (vector)60J25FOS: MathematicsState spaceApplied mathematicsWasserstein distance0101 mathematicsMathematicsProbability (math.PR)010102 general mathematicsErgodicityErgodicity[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Linear Differential EquationsPiecewisesymbolsJumpAMS-MSC. 60J75; 60J25; 93E15; 34D23Vector fieldStatistics Probability and Uncertainty60J75[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]Mathematics - Probability

description

International audience; We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.

yearjournalcountryeditionlanguage
2012-04-09
10.1214/ecp.v17-1932http://arxiv.org/abs/1204.1922