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Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
Controlling the stochastic dynamics of biological populations is a challenge that arises across various biological contexts. However, these dynamics are inherently nonlinear and involve a discrete state space, i.e., the number of molecules,…
This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…
In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
We consider discrete-time dynamical systems with a linear relaxation dynamics that are driven by deterministic chaotic forces. By perturbative expansion in a small time scale parameter, we derive from the Perron-Frobenius equation the…
We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics…
A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new…
The large deviations at various levels that are explicit for Markov jump processes satisfying detailed-balance are revisited in terms of the supersymmetric quantum Hamiltonian $H$ that can be obtained from the Markov generator via a…
We consider Hamiltonians associated to optimal control problems for affine systems on the torus. They are not coercive and are possibly unbounded from below in the direction of the drift of the system. The main assumption is the strong…
Using the modified Prelle- Singer approach, we point out that explicit time independent first integrals can be identified for the damped linear harmonic oscillator in different parameter regimes. Using these constants of motion, an…
Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are…
Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 large deviation {\em functional} characterizing the empirical density of the underlying…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
This paper is about operator-theoretic methods for solving nonlinear stochastic optimal control problems to global optimality. These methods leverage on the convex duality between optimally controlled diffusion processes and…
We study the large-time behaviour of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where…
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…