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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Markov Chains and θ-Congruent Number Problem
马尔可夫链 θ-同余数 θ-全等数分布
2023/5/10
A positive integer n is called a θ-congruent number if n sin θ is the area of a triangle with rational side lengths and with an angle θ. Markov chains play a key role in the study of the distribution ...
A Gaussian upper bound for the iterated kernels of Markov chains is obtained under some natural conditions. This result applies in particular to simple random walks on any locally compact unimodular g...
Chutes and Ladders in Markov Chains
Markov chains stationary distribution Bessel diffusions Sierspinski gasket
2015/7/14
We investigate how the stationary distribution of a Markov chain changes when
transitions from a single state are modified. In particular, adding a single
directed edge to nearest neighbor random wa...
Regular perturbation of V -geometrically ergodic Markov chains
Regular perturbation V -geometrically ergodic Markov chains Probability
2012/6/21
In this paper, new conditions for the stability of V-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller ...
Cover times for sequences of Markov chains on random graphs
Random walk Cover time Maximal hitting time Random graph
2012/6/15
We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (type 1) is the class of cover times approximated by the maximal hitting times s...
Tunneling and Metastability of continuous time Markov chains II, the nonreversible case
Metastability Tunneling Markov processes
2012/5/25
We proposed in \cite{bl2} a new approach to prove the metastable behavior of reversible dynamics based on potential theory and local ergodicity. In this article we extend this theory to nonreversible ...
Commuting time geometry of ergodic Markov chains
Commuting time geometry ergodic Markov chains Probability
2011/9/5
Abstract: We show how to map the states of an ergodic Markov chain to Euclidean space so that the squared distance between states is the expected commuting time. We find a minimax characterization of ...
Some Aspects of Modeling Dependence in Copula-based Markov chains
Markov chains copula mixing conditions reversible processes
2011/8/31
Abstract: Dependence coefficients have been widely studied for Markov processes defined by a set of transition probabilities and an initial distribution. This work clarifies some aspects of the theory...
Pointwise stabilization of discrete-time matrix-valued stationary Markov chains
Markovian jump linear system pointwise stabilization random products of matrices
2011/8/22
Abstract: Let $(\Omega,\mathscr{F},\mathbb{P})$ be a probability space and $\bS=\{\mathrm{S}_1,...,\mathrm{S}_K\}$ a discrete-topological space that consists of $K$ real $d$-by-$d$ matrices, where $K$...
Perfect Sampling of Markov Chains with Piecewise Homogeneous Events
Markov chains perfect sampling queueing systems
2011/3/2
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a nite time without ever computing the distribution.
Efficient Generation of Random Bits from Finite State Markov Chains
Efficient Generation of Random Bits Finite State Markov Chains
2011/2/25
The problem of random number generation from an uncorrelated random source (of unknown probability distribution)dates back to von Neumann’s 1951 work.
Central limit theorem for triangular arrays of Non-Homogeneous Markov chains
central limit theorem triangular arrays non-homogeneousMarkov chains
2011/3/1
In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on ma...
Entropy Rate for Hidden Markov Chains with rare transitions
Entropy Rate for Hidden Markov Chains rare transitions
2011/1/20
We consider Hidden Markov Chains obtained by passing a Markov Chain with rare transitions through a noisy memoryless channel. We obtain asymptotic estimates for the entropy of the resulting Hidden Mar...
Backward Stochastic Differential Equations with Markov Chains and The Application: Homogenization of PDEs System
BSDE Markov chain weak convergence homogenization
2010/12/13
Stemmed from the derivation of the optimal control to a stochastic linearquadratic control problem with Markov jumps, we study one kind of backward stochastic differential equations (BSDEs) that the g...
Filtering of continuous-time Markov chains with noise-free observation and applications
Filtering of continuous-time Markov chains noise-free observation applications
2010/11/30
Let X be a continuous-time Markov chain in a finite set I, let h be a mapping of I onto another set, and let Y be defined by Yt = h(Xt), (t ≥ 0). We address the filtering problem
for X in terms of th...