scholarly journals Exponential ergodicity in the bounded-Lipschitz distance for some piecewise-deterministic Markov processes with random switching between flows

2022 ◽  
Vol 215 ◽  
pp. 112678
Author(s):  
Dawid Czapla ◽  
Katarzyna Horbacz ◽  
Hanna Wojewódka-Ściążko
Keyword(s):  
Markov Processes ◽  
Exponential Ergodicity ◽  
Piecewise Deterministic Markov Processes ◽  
Random Switching

scholarly journals Exponential ergodicity for Markov processes with random switching

Bernoulli ◽  
2015 ◽  
Vol 21 (1) ◽  
pp. 505-536 ◽  
Author(s):  
Bertrand Cloez ◽  
Martin Hairer
Keyword(s):  
Markov Processes ◽  
Exponential Ergodicity ◽  
Random Switching

scholarly journals Random switching near bifurcations

2019 ◽  
Vol 20 (02) ◽  
pp. 2050008 ◽  
Author(s):  
Tobias Hurth ◽  
Christian Kuehn
Keyword(s):  
Markov Processes ◽  
Vector Fields ◽  
Invariant Measures ◽  
Blow Up ◽  
Nonlinear Models ◽  
Switching Dynamics ◽  
Piecewise Deterministic Markov Processes ◽  
Random Switching ◽  
Pitchfork Bifurcations

The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise-deterministic Markov processes arising from stochastic switching dynamics near fold, Hopf, transcritical and pitchfork bifurcations. We prove the existence of invariant measures for different switching rates. We also study when the invariant measures are unique, when multiple measures occur, when measures have smooth densities, and under which conditions finite-time blow-up occurs. We demonstrate the applicability of our results for three nonlinear models arising in applications.

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