Related papers: Strong diffusion approximation in averaging with d…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…
We investigate the homogeneous Dirichlet problem for the Fast Diffusion Equation $u_t=\Delta u^m$, posed in a smooth bounded domain $\Omega\subset \mathbb{R}^N$, in the exponent range $m_s=(N-2)_+/(N+2)<m<1$. It is known that bounded…
We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the…
We present a systematic theory of dissipation in finite Fermi systems like nuclei and metallic clusters. This theory is based on the application of semiclassical methods and random matrix theory to linear response of many-body systems. The…
We present results on spatio-temporal correlations in the so-called mean drag version of the Durian bubble model in the limit of small, but finite, shearing rates, $\dot{\gamma}$. We study the rheology, diffusion, and spatial correlations…
We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…
The purpose of this paper is to investigate the long time behaviour for a self-interacting diffusion and a self-interacting velocity jump process. While the diffusion case has already been studied for some particular potential function, the…
The dynamics of a freely diffusing particle in a two-dimensional channel with cross sectional area $A(x)$, can be effectively described by a one-dimensional diffusion equation under the action of a potential of mean force $U(x)=-k_BT\ln…
We show that {\it strong} anomalous diffusion, i.e. $\mean{|x(t)|^q} \sim t^{q \nu(q)}$ where $q \nu(q)$ is a nonlinear function of $q$, is a generic phenomenon within a class of generalized continuous-time random walks. For such class of…
A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these…
Herein we develop a dynamical foundation for fractional Brownian Motion. A clear relation is established between the asymptotic behaviour of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
We suggest the diffuse approach to the relaxation processes within the kinetic theory for the Wigner distribution function. The diffusion and drift coefficients are evaluated taking into consideration the interparticle collisions on the…
Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…
Given an one-dimensional positive recurrent diffusion governed by the Stratonovich SDE \[ X_t=x+\int_0^t\sigma(X_s)\strat db(s)+\int_0^t m(X_s) ds, \] we show that the associated stochastic flow of diffeomorphisms focuses as fast as $…
Cox processes model overdispersed point process data via a latent stochastic intensity, but both nonparametric estimation of the intensity model and posterior inference over intensity paths are typically intractable, relying on expensive…
We consider a diffusion equation in $\mathbb{R}^d$ with drift equal to the gradient of a homogeneous potential of degree $1+\gamma$, with $0<\gamma<1$, and local variance equal to $\varepsilon^2$ with $\varepsilon\to 0$. The associated…