Related papers: Weak Error of Dean-Kawasaki Equation with Smooth M…
We give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilizing and developing the stochastic sewing lemma of L\^e (2020). This approach allows one to exploit regularization by noise effects…
In this paper, by utilizing Wang's Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for McKean-Vlasov SDEs with integrable drift is investigated. In addition, using the decoupled method, some…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
We prove that the Dean-Kawasaki SPDE admits a solution only in integer parameter regimes, in which case the solution is given in terms of non-interacting particles.
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
The Dean-Kawasaki equation - a strongly singular SPDE - is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of $N$ independent diffusing particles in…
We consider Mckean-Vlasov type stochastic differential equations with multiplicative noise arising from the random vortex method. Such an equation can be viewed as the mean-field limit of interacting particle systems with singular…
This paper studies the weak convergence order of the stochastic theta method for stochastic differential equations (SDEs) driven by time-changed L\'{e}vy noise under global Lipschitz and linear growth conditions. In contrast to classical…
The purpose of this paper is to establish a well-posedness theory for conservative stochastic partial differential equations on the whole space. This class of stochastic PDEs arises in fluctuating hydrodynamics, and includes the…
We consider stochastic particle dynamics on hypersurfaces represented in Monge gauge parametrization. Starting from the underlying Langevin system, we derive the surface Dean-Kawasaki (DK) equation and formulate it in the martingale sense.…
We study two interacting particle systems, both modeled as a system of $N$ stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate…
Strong convergence rates for numerical approximations of semilinear stochastic partial differential equations (SPDEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for numerical…
In this article, we establish the \textsl{Wong-Zakai approximation} result for a class of stochastic partial differential equations (SPDEs) with fully local monotone coefficients perturbed by a multiplicative Wiener noise. This class of…
In the past decade, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that has discontinuities in space has begun. In the majority of these results it is assumed that the drift…
Computing analytically the $n$-point density correlations in systems of interacting particles is a long-standing problem of statistical physics, with a broad range of applications, from the interpretation of scattering experiments in simple…
This work is devoted to averaging principle of a two-time-scale stochastic partial differential equation on a bounded interval $[0, l]$, where both the fast and slow components are directly perturbed by additive noises. Under some regular…
The strong well-posedness of the Vlasov-Fokker-Planck-Dean-Kawasaki (VFPDK) equation with correlated noise is established. This equation can be interpreted as the fluctuating mean-field limit of second-order Newtonian particle systems,…
A wide range of phenomena in the natural and social sciences involve large systems of interacting particles, including plasmas, collections of galaxies, coupled oscillators, cell aggregations, and economic ``agents'. Kinetic methods for…
The results of the author and Gess [27] develop a robust well-posedness theory for a broad class of conservative stochastic PDEs, with both probabilistically stationary and non-stationary Stratonovich noise, and with irregular noise…
We consider a L\'evy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain…