scholarly journals Rates of convergence to equilibrium for potlatch and smoothing processes

2021 ◽  
Vol 49 (3) ◽  
Author(s):  
Sayan Banerjee ◽  
Krzysztof Burdzy
Keyword(s):  
Rates Of Convergence ◽  
Convergence To Equilibrium

scholarly journals On the rates of convergence of Erlang's model

1999 ◽  
Vol 36 (4) ◽  
pp. 1167-1184 ◽  
Author(s):  
Christine Fricker ◽  
Philippe Robert ◽  
Danielle Tibi
Keyword(s):  
Rates Of Convergence ◽  
Upper Bounds ◽  
Probabilistic Methods ◽  
Convergence To Equilibrium ◽  
Coupling Techniques

The convergence to equilibrium of the renormalized M/M/N/N queue is analysed. Upper bounds on the distance to equilibrium are obtained and the cut-off property for two regimes of this queue is proved. Simple probabilistic methods, such as coupling techniques and martingales, are used to obtain these results.

Rate of convergence to equilibrium of marked Hawkes processes

2002 ◽  
Vol 39 (1) ◽  
pp. 123-136 ◽  
Author(s):  
P. Brémaud ◽  
G. Nappo ◽  
G. L. Torrisi
Keyword(s):  
Rate Of Convergence ◽  
Stationary Process ◽  
Rates Of Convergence ◽  
Stopping Rules ◽  
Convergence To Equilibrium ◽  
Situation Models ◽  
Hawkes Process ◽  
Hawkes Processes ◽  
Simulation Algorithms

In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

scholarly journals On the rates of convergence of Erlang's model

1999 ◽  
Vol 36 (04) ◽  
pp. 1167-1184 ◽  
Author(s):  
Christine Fricker ◽  
Philippe Robert ◽  
Danielle Tibi
Keyword(s):  
Rates Of Convergence ◽  
Upper Bounds ◽  
Probabilistic Methods ◽  
Convergence To Equilibrium ◽  
Coupling Techniques

The convergence to equilibrium of the renormalized M/M/N/N queue is analysed. Upper bounds on the distance to equilibrium are obtained and the cut-off property for two regimes of this queue is proved. Simple probabilistic methods, such as coupling techniques and martingales, are used to obtain these results.

Rate of convergence to equilibrium of marked Hawkes processes

2002 ◽  
Vol 39 (01) ◽  
pp. 123-136 ◽  
Author(s):  
P. Brémaud ◽  
G. Nappo ◽  
G. L. Torrisi
Keyword(s):  
Rate Of Convergence ◽  
Stationary Process ◽  
Rates Of Convergence ◽  
Stopping Rules ◽  
Convergence To Equilibrium ◽  
Situation Models ◽  
Hawkes Process ◽  
Hawkes Processes ◽  
Simulation Algorithms

In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

scholarly journals Subgeometric rates of convergence for Markov processes under subordination

2017 ◽  
Vol 49 (1) ◽  
pp. 162-181 ◽  
Author(s):  
Chang-Song Deng ◽  
René L. Schilling ◽  
Yan-Hong Song
Keyword(s):  
Markov Process ◽  
Invariant Measure ◽  
Convergence Rate ◽  
Rate Of Convergence ◽  
Rates Of Convergence ◽  
Bernstein Function ◽  
Convergence To Equilibrium ◽  
Speed Of Convergence ◽  
Crucial Point ◽  
Original Process

Abstract We are interested in the rate of convergence of a subordinate Markov process to its invariant measure. Given a subordinator and the corresponding Bernstein function (Laplace exponent), we characterize the convergence rate of the subordinate Markov process; the key ingredients are the rate of convergence of the original process and the (inverse of the) Bernstein function. At a technical level, the crucial point is to bound three types of moment (subexponential, algebraic, and logarithmic) for subordinators as time t tends to ∞. We also discuss some concrete models and we show that subordination can dramatically change the speed of convergence to equilibrium.

scholarly journals Uniform moment propagation for the Becker--Döring equations

2018 ◽  
Vol 149 (04) ◽  
pp. 995-1015
Author(s):  
José A. Cãnizo ◽  
Amit Einav ◽  
Bertrand Lods
Keyword(s):  
Maximum Principle ◽  
Rates Of Convergence ◽  
Convergence To Equilibrium ◽  
Stretched Exponential ◽  
The Maximum Principle ◽  
Exponential Moments ◽  
Time Propagation

AbstractWe show uniform-in-time propagation of algebraic and stretched exponential moments for the Becker--Döring equations. Our proof is based upon a suitable use of the maximum principle together with known rates of convergence to equilibrium.

The entropy dissipation method for spatially inhomogeneous reaction–diffusion-type systems

2008 ◽  
Vol 464 (2100) ◽  
pp. 3273-3300 ◽  
Author(s):  
Marco Di Francesco ◽  
Klemens Fellner ◽  
Peter A Markowich
Keyword(s):  
Reaction Diffusion ◽  
Nonlinear Problems ◽  
Type Systems ◽  
Rates Of Convergence ◽  
Energy Functional ◽  
Convergence To Equilibrium ◽  
Solid State Physics ◽  
Diffusion Type ◽  
Entropy Dissipation ◽  
Diffusion Convection

We study the long-time asymptotics of reaction–diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion–convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction–diffusion–convection system arising in solid-state physics as a paradigm for general nonlinear systems.

Sign in / Sign up

Export Citation Format

Share Document