Related papers: Stochastic Integral Representation for the Dynamic…
The main subject of the thesis is the study of stationary nonequilibrium states trough the use of microscopic stochastic models that encode the physical interaction in the rules of Markovian dynamics for particles configurations. These…
We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the…
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
Statistical measures of chaos have long been used in the study of chaotic dynamics in the framework of the interacting boson model. The use of large number of bosons renders additional studies of chaos possible, that can provide a direct…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
We study stochastic perturbations of linear systems of the form $$ dv(t)+Av(t)dt = \epsilon P(v(t))dt+\sqrt{\epsilon}B(v(t)) dW (t), v\in\mathbb{R}^{D}, (*) $$ where $A$ is a linear operator with non-zero imaginary spectrum. It is assumed…
These notes attempt a self-contained introduction into statistical field theory applied to neural networks of rate units and binary spins. The presentation consists of three parts: First, the introduction of fundamental notions of…
We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean field theory (DMFT) and the equilibrium coherent potential approximation (CPA)…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…
An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival…