Related papers: On stochastic Euler-Poincar\'{e} equations driven …

This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the…

In this paper, we first show the well-posedness of the SDEs driven by L\'{e}vy noises under mild conditions. Then, we consider the existence and uniqueness of periodic solutions of the SDEs. To establish the ergodicity and uniqueness of…

We introduce the notion of stochastic logarithmic Lipschitz constants and use these constants to characterize stochastic contractivity of It\^o stochastic differential equations (SDEs) with multiplicative noise. We find an upper bound for…

We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…

In this paper, we show the existence and uniqueness of a strong solution to stochastic 3D tamed Navier-Stokes equations driven by multiplicative Levy noise with periodic boundary conditions. Then we establish the large deviation principles…

In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier--Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically…

We study the focusing stochastic nonlinear Schr\"odinger equation in one spatial dimension with multiplicative noise, driven by a Wiener process white in time and colored in space, in the $L^2$-critical and supercritical cases. The mass…

We analyze the numerical solutions of a stochastic Arctic sea ice model with multiplicative noise over a wide range of external heat-fluxes, $\Delta F_0$, which correspond to greenhouse gas forcing. When the noise is multiplicative, the…

Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a…

The stochastic differential equation $\dot{x}(t) = ax(t) + bx(t-\tau) + c x(t) \xi(t)$ with a time-delayed feedback and a multiplicative Gaussian noise is shown to be related to Kardar-Parisi-Zhang universality class of growing surfaces.

We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently…

By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong Feller property and heat kernel…

We study a new class of McKean-Vlasov stochastic differential equations (SDEs), possibly with common noise, applying the theory of time-inhomogeneous polynomial processes. The drift and volatility coefficients of these SDEs depend on the…

In this paper, we study a class of slow-fast stochastic partial differential equations with multiplicative Wiener noise. Under some appropriate conditions, we prove the slow component converges to the solution of the corresponding averaged…

Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our…

Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…

We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…

Recent advancements in machine learning have transformed the discovery of physical laws, moving from manual derivation to data-driven methods that simultaneously learn both the structure and parameters of governing equations. This shift…

This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…

We derive the equations of nonlinear electroelastostatics using three different variational formulations involving the deformation function and an independent field variable representing the electric character - considering either one of…