Related papers: Markov evolutions and hierarchical equations in th…
We discuss general concept of Markov statistical dynamics in the continuum. For a class of spatial birth-and-death models, we develop a perturbative technique for the construction of statistical dynamics. Particular examples of such systems…
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
The evolution of states of a spatial ecological model is studied. The model describes an infinite population of point entities placed in $\mathbb{R}^d$ which reproduce themselves at distant points (disperse) and die with rate that includes…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
An exactly solvable model for the multi-level system interacting with several reservoirs at zero temperatures is presented. Population decay rates and decoherence rates predicted by exact solution and several approximate master equations,…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
This paper is the second of two papers devoted to the study of the evolution of the cosmological horizons (particle and event horizons). Specifically, in this paper we consider the extremely general case of an accelerated universe with…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
The quantum jump approach allows to characterize the stochastic dynamics associated to an open quantum system submitted to a continuous measurement action. In this paper we show that this formalism can consistently be extended to…
We propose a new form for the quantum master equation in the theory of open quantum systems. This new formalism allows one to describe the dynamics of two-level systems moving along different hyperbolic trajectories with distinct proper…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
The evolutions of states is described corresponding to the Glauber dynamics of an infinite system of interacting particles in continuum. The description is conducted on both micro- and mesoscopic levels. The microscopic description is based…
The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric…
We deal with two following classes of equilibrium stochastic dynamics of infinite particle systems in continuum: hopping particles (also called Kawasaki dynamics), i.e., a dynamics where each particle randomly hops over the space, and…
We examine a completely positive and trace preserving evolution of finite dimensional open quantum system, coupled to large environment via periodically modulated interaction Hamiltonian. We derive a corresponding Markovian Master Equation…
A master equation for the evolution of two-dimensional universe is derived based on the simplicial quantum gravity regarding the evolution as the Markov process of a space-time lattice. Three typical phases, expanding, elongating and…
A novel framework for the analysis of observation statistics on time discrete linear evolutions in Banach space is presented. The model differs from traditional models for stochastic processes and, in particular, clearly distinguishes…