scholarly journals Exact long time behavior of some regime switching stochastic processes

Bernoulli ◽  
2020 ◽  
Vol 26 (4) ◽  
pp. 2572-2604
Author(s):  
Filip Lindskog ◽  
Abhishek Pal Majumder
Keyword(s):  
Stochastic Processes ◽  
Regime Switching ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

Long-time behavior of Lévy-driven Ornstein–Uhlenbeck processes with regime switching

2020 ◽  
Vol 57 (1) ◽  
pp. 266-279
Author(s):  
Zhongwei Liao ◽  
Jinghai Shao
Keyword(s):  
Stationary Distribution ◽  
Regime Switching ◽  
Lévy Noise ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Lévy Measure ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Long Time ◽  
Levy Noise

AbstractWe investigate the long-time behavior of the Ornstein–Uhlenbeck process driven by Lévy noise with regime switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein–Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Lévy noise and the regime switching described by a Markov chain can derive the heavy-tailed property of the stationary distribution. The different role played by the Lévy measure and the regime-switching process is clearly characterized.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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