Related papers: One dimensional stable probability density functio…
We develop a new $L^1$ law of large numbers where the $i$-th summand is given by a function $h(\cdot)$ evaluated at $X_i - \theta_n$, and where $\theta_n \circeq \theta_n(X_1,X_2,\ldots,X_n)$ is an estimator converging in probability to…
In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of…
Fractional relaxation equations, as well as relaxation functions time-changed by independent stochastic processes have been widely studied (see, for example, \cite{MAI}, \cite{STAW} and \cite{GAR}). We start here by proving that the…
A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…
The one-dimensional propagation of seismic waves with constant Q is shown to be governed by an evolution equation of fractional order in time, which interpolates the heat equation and the wave equation. The fundamental solutions for the…
For Hill's equation on [0,infinity) we prove new characterizations of the spectral function rho(lambda) and the spectral density function f(lambda) based on analysis involving a companion system of first order differential equations in…
An inductive procedure is developed to calculate the asymptotic behavior at time zero of a diffusion with polynomial drift and degenerate, additive noise. The procedure gives rise to two different rescalings of the process; namely, a…
Recent advances in infinite-dimensional diffusion models have demonstrated their effectiveness and scalability in function generation tasks where the underlying structure is inherently infinite-dimensional. To accelerate inference in such…
We study the probability density function $P(h_m,L)$ of the maximum relative height $h_m$ in a wide class of one-dimensional solid-on-solid models of finite size $L$. For all these lattice models, in the large $L$ limit, a central limit…
We consider a diffusing particle, with diffusion constant D', moving in one dimension in an infinite sea of noninteracting mobile traps with diffusion constant D and density rho. We show that the asymptotic behavior of the survival…
The aim of this paper is to study the recovery of a spatially dependent potential in a (sub)diffusion equation from overposed final time data. We construct a monotone operator one of whose fixed points is the unknown potential. The…
We study the asymptotic behaviour of sharp front solutions arising from the nonlinear diffusion equation \theta_t = (D(\theta)\theta_x)_x, where the diffusivity is an exponential function D({\theta}) = D_o exp(\beta\theta). This problem…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…
We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…
In this report we investigate the regularity of the solution to the fractional diffusion, advection, reaction equation on a bounded domain in $\mathbb{R}^{1}$. The analysis is performed in the weighted Sobolev spaces, $H_{(a ,…
Let $f(t_1,\ldots,t_n)$ be a nondegenerate integral quadratic form. We analyze the asymptotic behavior of the function $D_f(X)$, the number of integers of absolute value up to $X$ represented by $f$. When $f$ is isotropic or $n$ is at least…
We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a…
In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain $D$ of $ \mathbb{R}^{k}$, $k\ge 1$, which includes the fractional power $\mathcal L^\beta$, $0<\beta\le…