Related papers: On Markovian behaviour of $p$-adic random dynamica…
We study ergodic properties of some Markov chains models in random environments when the random Markov kernels that define the dynamic satisfy some usual drift and small set conditions but with random coefficients. In particular, we adapt a…
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events…
Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…
Based on some recent work of the author on stochastic approximation in non-markovian environments, the situation when the driving random process is non-ergodic in addition to being non-markovian is considered. Using this, we propose an…
Large dynamical fluctuations - atypical realizations of the dynamics sustained over long periods of time - can play a fundamental role in determining the properties of collective behavior of both classical and quantum non-equilibrium…
This paper deals with the question of how to most effectively conduct experiments in Partially Observed Markov Decision Processes so as to provide data that is most informative about a parameter of interest. Methods from Markov decision…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
We study a class of Markovian systems of $N$ elements taking values in $[0,1]$ that evolve in discrete time $t$ via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspired by variants of the…
We connect self-interacting processes, that is, stochastic processes where transitions depend on the time spent by a trajectory in each configuration, to Doob conditioning. In this way we demonstrate that Markov processes with constrained…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…
In this paper we investigate the behavior of trajectories of one class of rational $p$-adic dynamical systems in complex $p$-adic field $\C_p$. We studied Siegel disks and attractors of such dynamical systems. We found the basin of the…
Dynamics of information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for Markovian processes and study its behavior to observe information flow through the system. Examples of the…
The Markovian dynamics of a qubit is investigated in the scheme of random unitary dynamics, where Kraus operators are changed by an extra noise. The behavior of Markovianity is explored in the perturbed scenario. We provide a new algorithm…
The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…
Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although…
Repulsive and attractive interactions usually lead to very different physics. Striking exceptions exist in the dynamics of driven-dissipative quantum systems. For the example of a photonic Bose-Hubbard dimer, we establish a one-to-one…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…