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We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in…
The trajectories of diffusion processes are continuous but non-differentiable, and each occurs with vanishing probability. This introduces a gap between theory, where path probabilities are used in many contexts, and experiment, where only…
We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation algorithm, which combines statistical and computational efficiency in high-dimensions.…
We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety of questions in mathematical physics, our main…
The first arrivals among $N$ Brownian particles is ubiquitous in the life sciences, as it often trigger cellular processes from the molecular level. We study here the case where stochastic particles, which represent molecules, proteins or…
We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to…
The barrier-crossing event for superdiffusion characterized by symmetric L\'{e}vy flights is analyzed. Starting from the fractional Fokker-Planck equation, we derive an integro-differential equation along with the necessary conditions to…
We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We…
We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is…
This work is devoted to deriving the Onsager-Machlup action functional for stochastic partial differential equations with (non-Gaussian) Levy process as well as Gaussian Brownian motion. This is achieved by applying the Girsanov…
This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…
This paper presents a complete description of noise-induced decay of a metastable state in a wide range of noise intensity. Recurrent formulas of exact moments of decay time valid for arbitrary noise intensity have been obtained. The…
In this paper we consider systems of weakly interacting particles driven by colored noise in a bistable potential, and we study the effect of the correlation time of the noise on the bifurcation diagram for the equilibrium states. We…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
This paper studies the optimal tracking control problem for continuous-time stochastic linear systems with multiplicative noise. The solution framework involves solving a stochastic algebraic Riccati equation for the feedback gain and a…
The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena…
In [SIAM J. Appl. Dyn. Sys., 12(4):2068--2092, 2013], Widiasih proposed and analyzed a deterministic one-dimensional Budyko-Sellers energy-balance model with a moving ice-line. In this paper, we extend this model to the stochastic setting…
A thermodynamics for systems at a stationary states is formulated. It is based upon the assumption of the existence of local equilibrium in phase space which enables one to interpret the probability density ans its conjugated nonequilibrium…