Related papers: McKean-Vlasov limits of scaling-critical reaction-…

Reaction-diffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or Kolmogorov-Petrovsky-Piscounov equation. These equations have a continuous family of front solutions, each…

We study the solution to a nonlinear stochastic heat equation in $d\geq 3$. The equation is driven by a Gaussian multiplicative noise that is white in time and smooth in space. For a small coupling constant, we prove (i) the solution…

In this paper, we are interested in conditional McKean-Vlasov jump diffusions, which are also termed as McKean-Vlasov stochastic differential equations with jump idiosyncratic noise and jump common noise. As far as conditional McKean-Vlasov…

This paper is concerned with the analysis of blow-ups for two McKean-Vlasov equations involving hitting times. Let $(B(t); \, t \ge 0)$ be standard Brownian motion, and $\tau:= \inf\{t \ge 0: X(t) \le 0\}$ be the hitting time to zero of a…

In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin…

We investigate properties of the (conditional) law of the solution to SDEs driven by fractional Brownian noise with a singular, possibly distributional, drift. Our results on the law are twofold: i) we quantify the spatial regularity of the…

We investigate the conditional McKean-Vlasov stochastic differential equations with jumps and Markovian regime-switching. We establish the strong wellposedness using L2-Wasser-stein distance on the Wasserstein space. Also, we establish the…

We develop a mean-field theory for large, non-exchangeable particle (agent) systems where the states and interaction weights co-evolve in a coupled system of SDEs. A first main result is the establishment of the propagation of…

The goal of this paper is to supplement the large deviation principle of the Freidlin--Wentzell theory on exit problems for diffusion processes with results of classical central limit theorem kind. We describe a class of situations where…

We study through numerical simulation the spherical collapse of isothermal gas in Newtonian gravity. We observe a critical behavior which occurs at the threshold of gravitational instability leading to core formation. For a given initial…

We establish a scaling limit for autonomous stochastic Newton equations, the solutions are often called nonlinear stochastic oscillators, where the nonlinear drift includes a mean field term of McKean type and the driving noise is Gaussian.…

We consider a reaction-diffusion equation of the type \[ \partial_t\psi = \partial^2_x\psi + V(\psi) + \lambda\sigma(\psi)\dot{W} \qquad\text{on $(0\,,\infty)\times\mathbb{T}$}, \] subject to a "nice" initial value and periodic boundary,…

In this paper, we investigate a class of McKean-Vlasov stochastic differential equations under L\'evy-type perturbations. We first establish the existence and uniqueness theorem for solutions of the McKean-Vlasov stochastic differential…

We prove existence and uniqueness of the branch of the so-called \emph{anomalous eternal solutions} in exponential self-similar form for the subcritical fast-diffusion equation with a weighted reaction term $$ \partial_tu=\Delta…

Let $\xi(t\,,x)$ denote space-time white noise and consider a reaction-diffusion equation of the form \[ \dot{u}(t\,,x)=\tfrac12 u"(t\,,x) + b(u(t\,,x)) + \sigma(u(t\,,x)) \xi(t\,,x), \] on $\mathbb{R}_+\times[0\,,1]$, with homogeneous…

In the present paper, we study the existence and blow-up behavior to the following stochastic non-local reaction-diffusion equation: \begin{equation*} \left\{ \begin{aligned} du(t,x)&=\left[(\Delta+\gamma) u(t,x)+\int_{D}u^{q}(t,y)dy…

Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential…

We study the long time behavior of positive solutions of the Cauchy problem for nonlinear reaction-diffusion equations in $\mathbb{R}^N$ with bistable, ignition or monostable nonlinearities that exhibit threshold behavior. For $L^2$ initial…

The Obukhov-Corrsin theory of scalar turbulence [Obu49, Cor51] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analogue for passive scalars of Kolmogorov's K41 theory of fully…

We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be non-linear and path…