相关论文: Existence, uniqueness and convergence of a particl…
We study long time behavior of a discrete time weakly interacting particle system, and the corresponding nonlinear Markov process in $\mathbb{R}^d$, described in terms of a general stochastic evolution equation. In a setting where the state…
We show the existence of a self-similar solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard-spheres such that, whenever two particles meet, they either…
We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…
We develop a new approach to study the long time behaviour of solutions to nonlinear stochastic differential equations in the sense of McKean, as well as propagation of chaos for the corresponding mean-field particle system approximations.…
In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude…
We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
The no-pumping theorem states that seemingly natural driving cycles of stochastic machines fail to generate directed motion. Initially derived for single particle systems, the no-pumping theorem was recently extended to many-particle…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium…
In this thesis we study the lateral electrostatic interaction between a pair of non-identical, moderately charged colloidal particles trapped at an electrolyte interface in the limit of short inter-particle separations. Using a simplified…
We study strong existence and pathwise uniqueness for a class of infinite-dimensional singular stochastic differential equations (SDE), with state space as the cone $\{x \in \mathbb{R}^{\mathbb{N}}: -\infty < x_1 \leq x_2 \leq \cdots\}$,…
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an…
In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…
In this note we review recent results on existence and uniqueness of solutions of infinite-dimensional stochastic differential equations describing interacting Brownian motions on $\R^d$.
We consider a new class of interacting particle systems with a countable number of interacting components. The system represents the time evolution of the membrane potentials of an infinite set of interacting neurons. We prove the existence…
Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
In this paper, we concern a system of stochastic PDE's. Our system consists of two components. Each component evolves according to the sotchastic Allen-Cahn equation with a symmetric double well potential and with addtional small space-time…
We investigate a McKean-Vlasov stochastic differential equation with an additive common noise and in which the interaction is through the conditional expectation. We show that, in the presence of an additive individual noise, existence and…