Related papers: Stochastic modelling of nonlinear dynamical system…
Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a…
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 study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…
A Fokker-Planck equation approach for the treatment of non-Markovian stochastic processes is proposed. The approach is based on the introduction of fictitious trajectories sharing with the real ones their local structure and initial…
We develop a theory to calculate the effective phase diffusion coefficient and the mean phase velocity in periodically driven stochastic models with two discrete states. This theory is applied to a dichotomically driven Markovian two state…
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
This paper studies the limit of a kinetic evolution equation involving a small parameter and driven by a random process which also scales with the small parameter. In order to prove the convergence in distribution to the solution of a…
We introduce a scheme for deriving an optimally-parametrised Langevin dynamics of few collective variables from data generated in molecular dynamics simulations. The drift and the position-dependent diffusion profiles governing the Langevin…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. The pulses are assumed to move radially with fixed shape and amplitudes decaying…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
Markovian diffusion processes yield a system of conservation laws which couple various conditional expectation values (local moments). Solutions of that closed system of deterministic partial differential equations stand for a regular…
We introduce a single generative mechanism with which it is able to describe diverse non-stationary diffusions. A non-stationary Markovian replication process for steps is considered, for which we analytically derive time-evolution of the…
We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…
The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…