scholarly journals Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry

2018 ◽  
Vol 275 (9) ◽  
pp. 2404-2452 ◽  
Author(s):  
Mustapha Mokhtar-Kharroubi ◽  
David Seifert
Keyword(s):  
Kinetic Equations ◽  
Rates Of Convergence ◽  
Convergence To Equilibrium ◽  
Slab Geometry

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.

Electronic Structure Calculations of Σ5 Grain Boundaries in Cu

1990 ◽  
Vol 193 ◽  
Author(s):  
Erik C. Sowa ◽  
A. Gonis ◽  
X.-G. Zhang
Keyword(s):  
Electronic Structure ◽  
Grain Boundaries ◽  
Region Of Interest ◽  
Rates Of Convergence ◽  
Electronic Structure Calculations ◽  
Real Space ◽  
Slab Geometry ◽  
Translational Invariance ◽  
Integral Number ◽  
Structure Calculations

Extended AbstractIn a recent publication [1], we presented results of electronic-structure calculations on Σ5 grain boundaries in Cu. These calculations were performed using the real-space multiplescattering theory (RSMST), a first-principles method which does not rely on translational invariance and Bloch's theorem [2, 3], and hence avoids the problems associated with treating interfaces in a periodic repeating slab geometry. A brief summary of this method follows.The RSMST is based on the concept of semi-infinite periodicity (SIP), defined as the regular repetition along a given direction of a scattering unit (atom, planes of atoms, etc.), or a set of such units. Systems with SIP possess the property of removal invariance, which states that the scattering properties (scattering matrices) of any such system remain invariant when an integral number of scattering units is removed from, or added to, the free end of the system. Using this property in conjunction with multiple-scattering theory, one can determine the electronic Green function, and hence all one-particle quantities such as the density of states (DOS), directly in real space.The essence of the method consists in a prescription for the proper renormalization of the scattering properties of the boundary sites of a cluster of atoms. Unrenormalized or “bare” sites in the interior of the cluster describe the region of interest, such as a grain boundary, while the renormalized boundary sites represent the infinite medium surrounding the cluster. This “dressing up” of the cluster is done independently for each part of a system that is characterized by its own SIP, so that grain boundaries between essentially arbitrary crystal structures can be treated.The calculations described previously [1] used given atomistic configurations and electronic one-particle potentials and computed the local DOS at atoms of interest within the grain boundaries. We are currently extending our method to incorporate charge self-consistency and total-energy capabilities. In connection with this, we have implemented four different methods of expressing mathematically the invariance properties of semi-infinite systems, and are evaluating them for optimal rates of convergence and computational efficiency. Calculations on Cu (100) monolayers will be used to illustrate these methods.

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.

Sign in / Sign up

Export Citation Format

Share Document