First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing event. In this study, obtaining distribution of the first passage time relating to lumped states which are constructed by gathering the states through lumping method for a irreduci...

It is known that for memoryless sources, the average and maximal redundancy of fixed–to–variable length codes, such as the Shannon and Huffman codes, exhibit two modes of behavior for long blocks. It either converges to a limit or it has an oscillatory pattern, depending on the irrationality or rationality, respectively, of certain parameters that depend on the source. In this paper, we extend ...

Periodic and non-periodic components of electrophysiological signals are modelled in terms syncronized sequences closed loops firing neurons correlated according to a Markov chain. Single reproduce fundamental harmonic components, appearing as lines the power spectra at frequencies ranging from 0.5 Hz 100 Hz. Further interesting features brainwave emerge by considering multiple loops. In partic...

We consider irreducible reversible discrete time Markov chains on a finite state space. Mixing times and hitting times are fundamental parameters of the chain. We relate them by showing that the mixing time of the lazy chain is equivalent to the maximum over initial states x and large sets A of the hitting time of A starting from x. We also prove that the first time when averaging over two cons...

The age of information (AoI) has attracted increasing attentions as a new metric and tool to capture the timeliness reception freshness data, which is different from conventional such outage, delay, throughput. While most existing works focused on AoI analysis optimizing method, update system design by utilizing diversity reduce not fully exploited so far. Inspired this fact, novel status desig...

Investors use different approaches to select optimal portfolio. so, Optimal investment choices according to return can be interpreted in different models. The traditional approach to allocate portfolio selection called a mean - variance explains. Another approach is Markov chain. Markov chain is a random process without memory. This means that the conditional probability distribution of the nex...

We consider small bered perturbations of direct products of chaotic smooth interval maps. We prove that these multi-dimensional systems have a non-zero and nite number of invariant and ergodic probability measures with maximal entropy. We note that these dynamical systems are neither linear nor expansive. The proof uses a suitable generalization of Hofbauer's Markov diagram developped in 6] whi...

Let (X,P ) be an irreducible, random walk on the state space X which is at most countable. We suppose that the (usually infinite) stochastic matrix P describes a Markov chain {Zn}n∈N defined on a probability space (Ω,F ,P) with transition probabilities p(x, y) := P[Zn+1 = y|Zn = x] homogeneous in time. Besides we consider the n-step transition probabilities {p(x, y)}x,y∈X which represent the st...

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players’) equilibrium payoffs is independent of the state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile...