Related papers: Regularity and Stability for the Semigroup of Jump…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…
We provide a stochastic thermodynamic description across scales for $N$ identical units with all-to-all interactions that are driven away from equilibrium by different reservoirs and external forces. We start at the microscopic level with…
We consider a single Brownian particle in one dimension in a medium at a constant temperature in the underdamped regime. We stochastically reset the position of the Brownian particle to a fixed point in the space with a constant rate $r$…
We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently-observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M.…
We calculate the steady state distribution $P_{\text{SSD}}(\boldsymbol{X})$ of the position of a Brownian particle under an intermittent confining potential that switches on and off with a constant rate $\gamma$. We assume the external…
This paper aims to develop the stability theory for singular stochastic Markov jump systems with state-dependent noise, including both continuous- and discrete-time cases. The sufficient conditions for the existence and uniqueness of a…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
We study a compound Poisson (random time-change) approximation for stochastic differential equations (SDEs) and stochastic Volterra equations whose coefficients may be merely measurable in time and may even exhibit integrable singularities.…
We prove a generalised second-order Boltzmann-Gibbs principle for conservative interacting particle systems on a lattice whose stationary measures are not of product type and not invariant under particle jumps. The result, which requires…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general…
In this paper, we consider a general time-inconsistent optimal control problem for a non homogeneous linear system, in which its state evolves according to a stochastic differential equation with deterministic coefficients, when the noise…
The semiclassical Boltzmann equation is widely used to study transport effects. However, being semiclassical and borrowing heavily from classical mechanics, the formalism calls for verification from the perspective of quantum mechanics.…
We consider n-point sticky Brownian motions: a family of n diffusions that evolve as independent Brownian motions when they are apart, and interact locally so that the set of coincidence times has positive Lebesgue measure with positive…
In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just…
Owing to the Chapman-Kolmogorov equation for Markovian dynamics,any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states. This property…
In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of semi-Markov processes is established. The variable order…
We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson…
We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random…
Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data motivate the use of mathematical models to characterise the motion…