Related papers: Vlasov scaling for stochastic dynamics of continuo…
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase space due to their better scalability than continuum approaches with respect to dimension. Complex processes…
There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
In this paper, we investigate a special class of stochastic Markov processes, known as Glauber dynamics. Markov processes are importance, for example, in the study of complex systems. For this, we present the basic theory of Glauber…
The methods developed by authors are applied to some reductions of BBGKY hierarchy, namely, various examples of Vlasov-like systems which are important both for fusion modeling and for particular physical problems related to plasma/beam…
A semiclassical theory of linear response in finite Fermi systems, based on the Vlasov equation, and its applications to the study of isoscalar vibrations in heavy nuclei are reviewed. It is argued that the Vlasov equation can be used to…
Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…
One of the proposed solutions to the equilibrium selection problem for agents learning in repeated games is obtained via the notion of stochastic stability. Learning algorithms are perturbed so that the Markov chain underlying the learning…
A new modified Vlasov equation has been obtained in this paper for the systems with dissipative phenomena such as, for example, plasma with irradiation.
Molecule- and particle-based simulations provide the tools to test, in microscopic detail, the validity of classical nucleation theory. In this endeavour, determining nucleation mechanisms and rates for phase separation requires an…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
We present a method to determine the equilibrium geometry of large atomistic systems with linear scaling. It is based on a separate treatment of long and short wavelength components of the forces. While the rapidly varying part is handled…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest…
Multivariate stochastic volatility models with skew distributions are proposed. Exploiting Cholesky stochastic volatility modeling, univariate stochastic volatility processes with leverage effect and generalized hyperbolic skew…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact…