相关论文: On some mixing properties of copula-based Markov c…

In this paper we introduce some new copulas emerging from shock models. It was shown earlier that reflected maxmin copulas (RMM for short) are not just some specific singular copulas; they contain many important absolutely continuous…

The dynamics of a power system with a significant presence of renewable energy resources are growing increasingly nonlinear. This nonlinearity is a result of the intermittent nature of these resources and the switching behavior of their…

A rigorous and largely self-contained account of (a) the bread-and-butter concepts and techniques in Markov chain theory and (b) the long-term behaviour of chains. As much as possible, the treatment is probabilistic instead of analytical (I…

In this article, we prove that a small random perturbation of dynamical system with multiple stable equilibria converges to a Markov chain whose states are neighborhoods of the deepest stable equilibria, under a suitable time-rescaling,…

This paper considers large families of Markov chains (MCs) that are defined over a set of parameters with finite discrete domains. Such families occur in software product lines, planning under partial observability, and sketching of…

Theorems from Part 1 of this paper are generalized to {\psi}-mixing sources in this paper. Application to Markoff chains and order m Markoff chains is presented. The main result is the generalization of Theorem 1 in Part 1.

We develop a general theory for Markov chains whose transition probabilities are the coefficients of descent operators on combinatorial Hopf algebras. These model the breaking-then-recombining of combinational objects. Examples include the…

There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…

Considering a Markov chain defined on a cycle, near-quadratic improvement of mixing is shown when only a subtle perturbation is introduced to the structure and non-reversible transition probabilities are used. More precisely, a mixing time…

In systems of programmable matter, we are given a collection of simple computation elements (or particles) with limited (constant-size) memory. We are interested in when they can self-organize to solve system-wide problems of movement,…

The hitting and mixing times are two fundamental quantities associated with Markov chains. In Peres and Sousi[PS2015] and Oliveira[Oli2012], the authors show that the mixing times and "worst-case" hitting times of reversible Markov chains…

A $k$-height on a graph $G=(V, E)$ is an assignment $V\to\{0, \ldots, k\}$ such that the value on ajacent vertices differs by at most $1$. We study the Markov chain on $k$-heights that in each step selects a vertex at random, and, if…

A class of examples is constructed to show that for strictly stationary Markov chains that are reversible, the simultaneous mixing rates for the $\rho$-mixing and strong mixing ($\alpha$-mixing) conditions can be fairly arbitrary, within…

Several recent publications investigated Markov-chain modelling of linear optimization by a $(1,\lambda)$-ES, considering both unconstrained and linearly constrained optimization, and both constant and varying step size. All of them assume…

We introduce a Markov product structure for multivariate tail dependence functions, building upon the well-known Markov product for copulas. We investigate algebraic and monotonicity properties of this new product as well as its role in…

Modelling multivariate circular time series is considered. The cross-sectional and serial dependence is described by circulas, which are analogs of copulas for circular distributions. In order to obtain a simple expression of the dependence…

A Markov chain $X^i$ on a finite state space $S$ has transition matrix $P$ and initial state $i$. We may run the chains $(X^i: i\in S)$ in parallel, while insisting that any two such chains coalesce whenever they are simultaneously at the…

We introduce a family of copulas which are locally piecewise uniform in the interior of the unit cube of any given dimension. Within that family, the simultaneous control of tail dependencies of all projections to faces of the cube is…

The \emph{Mixed-Membership Stochastic Blockmodel (MMSB)} is a popular framework for modeling social network relationships. It can fully exploit each individual node's participation (or membership) in a social structure. Despite its powerful…

A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…