منابع مشابه
A PDE approach to finite time approximations in Ergodic Theory
For dynamical systems defined by vector fields over a compact invariant set, we introduce a new class of approximated first integrals based on finite-time averages and satisfying an explicit first order partial differential equation. Referring to the PDE framework, we detect their viscosity robustness with respect to stochastic perturbations of the vector field. We formulate this approximating ...
متن کاملNumerical Approximations for Stochastic Differential Games: The Ergodic Case
The Markov chain approximation method is a widely used, relatively easy to use, and efficient family of methods for the bulk of stochastic control problems in continuous time, for reßected-jump-diffusion type models. It has been shown to converge under broad conditions, and there are good algorithms for solving the numerical problems, if the dimension is not too high. We consider a class of sto...
متن کاملDiffusion Models and Steady-state Approximations for Exponentially Ergodic Markovian Queues by Itai Gurvich
Motivated by queues with many-servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove, approximates well that of the Markov chain. Strong approximations provide such “limitless” approximations for process dynamics. Our focus here is on steady-st...
متن کاملA Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations
Perturbations to Markov chains and Markov processes are considered. The unperturbed problem is assumed to be geometrically ergodic in the sense usually established through the use of Foster–Lyapunov drift conditions. The perturbations are assumed to be uniform, in a weak sense, on bounded time intervals. The long-time behavior of the perturbed chain is studied. Applications are given to numeric...
متن کاملErgodic theorem, ergodic theory, and statistical mechanics.
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Modelling
سال: 1980
ISSN: 0270-0255
DOI: 10.1016/0270-0255(80)90009-3