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We study the velocity of travelling waves of a reaction-diffusion system coupling a standard reaction-diffusion equation in a strip with a one-dimensional diffusion equation on a line. We show that it grows like the square root of the…

Analysis of PDEs · Mathematics 2015-07-02 Laurent Dietrich

We propose a definition of directional multivariate subexponential and convolution equivalent densities and find a useful characterization of these notions for a class of integrable and almost radial decreasing functions. We apply this…

Probability · Mathematics 2022-05-10 Kamil Kaleta , Daniel Ponikowski

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)…

Statistical Mechanics · Physics 2009-10-31 E. K. O. Hellen , T. P. Simula , M. J. Alava

Among all generalized Ornstein-Uhlenbeck processes which sample the same invariant measure and for which the same amount of randomness (a $N$-dimensional Brownian motion) is injected in the system, we prove that the asymptotic rate of…

Probability · Mathematics 2021-10-07 Arnaud Guillin , Pierre Monmarché

Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…

Probability · Mathematics 2025-05-27 Robert E. Gaunt , Zixin Ye

Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary…

Probability · Mathematics 2016-11-16 Andrey Sarantsev

We consider the problem of the discrete-time approximation of the solution of a one-dimensional SDE with piecewise locally Lipschitz drift and continuous diffusion coefficients with polynomial growth. In this paper, we study the strong…

Numerical Analysis · Mathematics 2024-05-03 Mireille Bossy , Kerlyns Martínez

We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…

Probability · Mathematics 2014-11-10 Ágnes Backhausz , Tamás F. Móri

We study large deviations asymptotics for a class of unbounded additive functionals, interpreted as normalized accumulated areas, of one-dimensional Langevin diffusions with sub-linear gradient drifts. Our results provide parametric…

Probability · Mathematics 2023-10-23 Mihail Bazhba , Jose Blanchet , Roger J. A. Laeven , Bert Zwart

Problems in exponential asymptotics are typically characterized by divergence of the associated asymptotic expansion in the form of a factorial divided by a power. In this paper, we demonstrate that in certain classes of problems that…

Classical Analysis and ODEs · Mathematics 2015-06-19 Philippe H. Trinh , S. Jonathan Chapman

A truncated sequential procedure is constructed for estimating the drift coefficient at a given state point based on discrete data of ergodic diffusion process. A nonasymptotic upper bound is obtained for a pointwise absolute error risk.…

Statistics Theory · Mathematics 2015-09-21 L. I. Galtchouk , S. M. Pergamenshchikov

This paper is concerned with a quantitative analysis of asymptotic behaviors of (possibly sign-changing) solutions to the Cauchy-Dirichlet problem for the fast diffusion equation posed on bounded domains with Sobolev subcritical exponents.…

Analysis of PDEs · Mathematics 2023-01-30 Goro Akagi

In this letter, we give a concise, closed-form expression for the differential entropy of the sum of two independent, non-identically-distributed exponential random variables. The derivation is straightforward, but such a concise entropy…

Information Theory · Computer Science 2016-09-12 Andrew W. Eckford , Peter J. Thomas

We calculate exponential growth constants describing the asymptotic behavior of several quantities enumerating classes of orientations of arrow variables on the bonds of several types of directed lattice strip graphs $G$ of finite width and…

Statistical Mechanics · Physics 2019-10-28 Shu-Chiuan Chang , Robert Shrock

We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak form of the limit equation is derived and the convergence of…

Analysis of PDEs · Mathematics 2014-07-31 Herbert Egger , Matthias Schlottbom

A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…

Statistical Mechanics · Physics 2017-10-13 Erik Aurell , Stefano Bo

We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…

Analysis of PDEs · Mathematics 2025-06-06 Henri Berestycki , Luca Rossi , Andrea Tellini

An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and…

Fluid Dynamics · Physics 2013-03-25 Len M. Pismen , Uwe Thiele

This paper is concerned with the Cauchy-Dirichlet problem for fast diffusion equations posed in bounded domains, where every energy solution vanishes in finite time and a suitably rescaled solution converges to an asymptotic profile.…

Analysis of PDEs · Mathematics 2023-12-05 Goro Akagi , Yasunori Maekawa

We establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics,…

Analysis of PDEs · Mathematics 2024-07-23 Ziyu Liu , Dongyi Wei , Shengquan Xiang , Zhifei Zhang , Jia-Cheng Zhao