The exit path of a Markov chain with rare transitions
The exit path of a Markov chain with rare transitions
We study the exit path from a general domain after the last visit to a set of a Markov chain with rare transitions. We prove several large deviation principles for the law of the succession of the cycles visited by the process (the cycle path), the succession of the saddle points gone through to jump from cycle to cycle on the cycle path (the saddle path) and the succession of all the points gone through (the exit path). We estimate the time the process spends in each cycle of the cycle path...
The island model as a Markov dynamic system
Parallel multi-deme genetic algorithms are especially advantageous because they allow reducing the time of computations and can perform a much broader search than single-population ones. However, their formal analysis does not seem to have been studied exhaustively enough. In this paper we propose a mathematical framework describing a wide class of island-like strategies as a stationary Markov chain. Our approach uses extensively the modeling principles introduced by Vose, Rudolph and their collaborators....
The Kiefer-Wolfowitz approximation method in controlled Markov chains
The logarithmic Sobolev constant of some finite Markov chains
The logarithmic Sobolev constant is always bounded above by half the spectral gap. It is natural to ask when this inequality is an equality. We consider this question in the context of reversible Markov chains on small finite state spaces. In particular, we prove that equality holds for simple random walk on the five cycle and we discuss assorted families of chains on three and four points.
The Markov chain asymptotics of random mapping graphs
The principle of truncations in applied probability
The Q-matrix problem 2 : Kolmogorov backward equations
The scaling limit of senile reinforced random walk.
The Shannon information on a Markov chain approximately normally distributed
The tail structure of nonhomogeneous finite state Markov chains: survey
Théorème local pour chaînes de Markov de probabilité de transition quasi-compacte. Applications aux chaînes V-géométriquement ergodiques et aux modèles itératifs
Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov
Theoretical analysis of steady state genetic algorithms
Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are...
Théorie spectrale d'un opérateur de transition sur un espace métrique compact
Three-dimensional reflected driftless random walks in troughs : new asymptotic behavior
Transforming stochastic matrices for stochastic comparison with the st-order
We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
Transforming stochastic matrices for stochastic comparison with the st-order
We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
Transient analysis in discrete time of Markovian queues with quadratic rates.
Transient and stationary characteristics of a packet buffer modelled as an map/sm/1/b system