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We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
Consider the following stochastic reaction-diffusion equation with logarithmic superlinear coefficient b, driven by space-time white noise W: $$ u_t(t,x) = (1/2)u_{xx}(t,x) + b(u(t,x)) + \sigma(u(t,x))W(dt,dx) $$ for $t > 0$ and $x \in…
We consider an infinite-dimensional dynamical system with polynomial nonlinearity and additive noise given by a finite number of Wiener processes. By studying how randomness is spread by the system we develop a counterpart of Hormander's…
This paper studies path stabilities of the solution to stochastic differential equations (SDE) driven by time-changed L\'evy noise. The conditions for the solution of time-changed SDE to be path stable and exponentially path stable are…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
We consider the mixed formulation of the equations governing Darcy-Forchheimer flow in porous media. We prove existence and uniqueness of a solution for the stationary problem and the existence of a solution for the transient problem.
In this paper we study a nonlinear stochastic fluid-structure interaction problem with a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a…
The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular…
In this paper we study the stochastic inhomogeneous incompressible Euler equations in the whole space $\RR^3$. We prove the existence and pathwise uniqueness of local solutions with both additive and multiplicative stochastic noise. Our…
We study the uniqueness in the path-by-path sense (i.e. $\omega$-by-$\omega$) of solutions to stochastic differential equations with additive noise and non-Lipschitz autonomous drift. The notion of path-by-path solution involves considering…
We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global…
Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic…
In this work, we demonstrate well-posedness and regularisation by noise results for a class of geometric transport equations that contains, among others, the linear transport and continuity equations. This class is known as linear advection…
We study stochastic dynamical systems in settings where only partial statistical information about the noise is available, e.g., in the form of a limited number of noise realizations. Such systems are particularly challenging to analyze and…
The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…
The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative,…
Recent experiments have probed the relative likelihoods of trajectories in stochastic systems by observing survival probabilities within a tube of radius $R$ in spacetime. We measure such probabilities here for a colloidal particle in a…
In this paper, we consider the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise. By assuming the ionic species have the same diffusivity and opposite valences, we prove the global well-posedness of the system.…
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between the mechanical pressure and the cell density, the model can…