Related papers: Modelling Illiquid Stocks Using Quantum Stochastic…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. We derive the global well-posedness result with instantaneous smoothness effect,…
The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…
While accurate simulations of dense gas flows far from the equilibrium can be achieved by Direct Simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order…
We investigate the effects of relatively rapid variations of the boundaries of an overmoded cavity on the stochastic properties of its interior acoustic or electromagnetic field. For quasi-static variations, this field can be represented as…
Given a solution of a nonlinear wave equation on the flat space-time (with a real analytic nonlinearity), we relate its Cauchy data at two different times by nonlinear representation formulas in terms of asymptotic series. We first show how…
Over the last decade, nonparametric methods have gained increasing attention for modeling complex data structures due to their flexibility and minimal structural assumptions. In this paper, we study a general multivariate nonparametric…
Starting from microscopic interaction rules we derive kinetic models of Fokker--Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the corresponding Boltzmann model. As particular cases,…
We introduce an efficient method to simulate dynamics of an interacting quantum impurity coupled to non-interacting fermionic reservoirs. Viewing the impurity as an open quantum system, we describe the reservoirs by their Feynman-Vernon…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
To describe stochastic quantum processes I propose an integral equation of Volterra type which is not generally transformable to any differential one. The process is a composition of ordinary quantum evolution which admits presence of a…
A possible approach to description of the non equilibrium system has been proposed. Based on the Fokker-Plank equation in term of energy for non equilibrium distribution function of macroscopical system was obtained the stationary solution…
A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…
In this work, our prime focus is to study the one to one correspondence between the conduction phenomena in electrical wires with impurity and the scattering events responsible for particle production during stochastic inflation and…
We consider the development of high order asymptotic-preserving linear multistep methods for kinetic equations and related problems. The methods are first developed for BGK-like kinetic models and then extended to the case of the full…
We recently showed that the S&P500 stock market index is well described by Tsallis non-extensive statistics and nonlinear Fokker-Planck time evolution. We argued that these results should be applicable to a broad range of markets and…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
Stochastic nonequilibrium exclusion models are treated using a real space scaling approach. The method exploits the mapping between nonequilibrium and quantum systems, and it is developed to accommodate conservation laws and duality…
We consider several stochastic service systems, and study the asymptotic behavior of the moments of various quantities that have application to models for random interval graphs and algorithms for searching for an idle server or empty…
Stochastic differential equations play an important role in various applications when modeling systems that have either random perturbations or chaotic dynamics at faster time scales. The time evolution of the probability distribution of a…