Related papers: Stochastic representation of deterministic interac…
How does one introduce randomness into a classical dynamical system in order to produce something which is related to the `corresponding' quantum system? We consider this question from a probabilistic point of view, in the context of some…
We study integral representations of random variables with respect to general H\"older continuous processes and with respect to two particular cases; fractional Brownian motion and mixed fractional Brownian motion. We prove that arbitrary…
We express the probabilistic character associated to the wave function by treating it as a stochastic variable. This is accomplished by means of a stochastic equation for the wave function whose noise changes the phase of the wave function…
We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…
A model of Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion, is discussed. The general dynamics outlined in Sect. 2 is…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical…
Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
Stochastic models of varying complexity have been proposed to describe the dispersion of particles in turbulent flows, from simple Brownian motion to complex temporally and spatially correlated models. A method is needed to compare…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for It\^{o} processes. These processes for…
We prove that deterministic motion in dissipative systems emerges as a strict geometric attractor of contact flow, not a statistical approximation. Building on the contact geometry of stochastic vector bundles, we develop time-dependent…
We review probabilistic approaches to the Gross-Pitaevskii theory describing interacting dilute systems of particles. The main achievement are large deviations principles for the mean occupation measure of a large system of interacting…