相关论文: Superdiffusive limits for Bessel-driven stochastic…
We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
We derive an anomalous, sub-diffusive scaling limit for a one-dimensional version of the Mott random walk. The limiting process can be viewed heuristically as a one-dimensional diffusion with an absolutely continuous speed measure and a…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with emphasis on the analytical formulation of the problem as well as a possible…
We introduce a class of one dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative…
In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric…
Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
This paper studies the limit of a kinetic evolution equation involving a small parameter and driven by a random process which also scales with the small parameter. In order to prove the convergence in distribution to the solution of a…
We analyze diffusion processes with finite propagation speed in a non-homogeneous medium in terms of the heterogeneous telegrapher's equation. In the diffusion limit of infinite-velocity propagation we recover the results for the…
Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the…
In this paper, we show that suitable transport noises produce anomalous dissipation of both enstrophy of solutions to 2D Navier-Stokes equations and of energy of solutions to diffusion equations in all dimensions. The key ingredients are…
The objective of this dissertation is to prove a scaling limit for the exit of a domain problem of a small noise system with underlying hyperbolic dynamics. In this case, Large Deviation kind of estimates fail to provide a complete picture…
Until very recently, the asymptotic occurrence of intrinsic anomalous scaling has been expected to require concomitant effects for kinetically rough interfaces, like quenched disorder or morphological instabilities. However, counterexamples…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
Stochastic Stokes' drift and hypersensitive transport driven by dichotomous noise are theoretically investigated. Explicit mathematical expressions for the asymptotic probability density and drift velocity are derived including the…
We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…
We study anomalous dissipation in the context of passive scalars and we construct a two-dimensional autonomous divergence-free velocity field in $C^\alpha$ (with $\alpha \in (0,1)$ arbitrary but fixed) which exhibits anomalous dissipation.…
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…