Recently, in [11], the “coin-turning walk” was introduced on Z. It is a non-Markovian process where steps form (possibly) time-inhomogeneous Markov chain. In this article, we follow up investigation by introducing analogous processes Zd,d≥2: at time n direction of “updated” with probability pn; otherwise next step repeats previous one. We study some fundamental properties these walks, such as t...

The Mori-Zwanzig formalism for coarse-graining a complex dynamical system typically introduces memory effects. The Markovian assumption of delta-correlated fluctuating forces is often employed to simplify the formulation of coarse-grained (CG) models and numerical implementations. However, when the time scales of a system are not clearly separated, the memory effects become strong and the Marko...

The dissipative dynamics of the spin chain coupled to non-Markovian magnonic reservoir was studied. chirality is formed due magnetoelectric coupling. We explored sign trace distance derivative and found alternating positive/negative periods in system's time evolution. negative associated with flow information from system bath decrease states distinguishability, while positive related opposite d...

We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of Markovian regime-switching. first prove existence unique global positive solution, and find invariant set for system. Then, we sufficient conditions a.s. extinction permanence, showing also their relation with stationary probability distribution Markov chain that governs switching netw...

Humans can learn under a wide variety of feedback conditions. Particularly important types of learning fall under the category of reinforcement learning (RL) where a series of decisions must be made and a sparse feedback signal is obtained. Computational and behavioral studies of RL have focused mainly on Markovian decision processes (MDPs), where the next state and reward depends only on the c...

Abstract: In this paper we discuss stochastic differential delay equations with Markovian switching. Such an equation can be regarded as the result of several stochastic differential delay equations switching from one to the others according to the movement of a Markov chain. The main aim of this paper is to investigate the robustness of exponential stability of the equations. The criteria obta...

This paper demonstrates that a proper design of environmental-regulation pricing strategies is able to promote Extended Product Responsibility for green supply chain firms in a competitive market. A differential game model comprising Vidale-Wolfe equation has been established in light of sales competition and recycling dynamics as well as regulation related profit function. Analytic solutions o...