Related papers: Mapping spatial persistent large deviations of non…
We consider a class of stochastic kinetic equations, depending on two time scale separation parameters $\epsilon$ and $\delta$: the evolution equation contains singular terms with respect to $\epsilon$, and is driven by a fast ergodic…
Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential…
In this paper, we study the discrete-time quantum random walks on a line subject to decoherence. The convergence of the rescaled position probability distribution $p(x,t)$ depends mainly on the spectrum of the superoperator…
In recent years several local extrema based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work we study systematically the distribution of the…
We consider the $N$-particle noncolliding Bernoulli random walk --- a discrete time Markov process in $\mathbb{Z}^{N}$ obtained from a collection of $N$ independent simple random walks with steps $\in\{0,1\}$ by conditioning that they never…
In order to give quantitative estimates for approximating the ergodic limit, we investigate probabilistic limit behaviors of time-averaging estimators of numerical discretizations for a class of time-homogeneous Markov processes, by…
The large deviations properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by N. R. Smith, Phys. Rev. E 106, L042202 (2022) and by R. Gutierrez, A. Canella-Ortiz, C. Perez-Espigares,…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
We study analytically the order statistics of a time series generated by the successive positions of a symmetric random walk of n steps with step lengths of finite variance \sigma^2. We show that the statistics of the gap d_{k,n}=M_{k,n}…
This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected to the Kendall convolution. In particular, based on its stochastic representation, we provide…
Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like <exp(i int_0^t Q(s)ds)>, where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets…
In this paper, we study the long-time stability behavior of a class of linear stochastic evolution equations in a Hilbert space with multiplicative noise. Explicit sufficient conditions for $p$-th moment and almost sure exponential…
Understanding the causes and effects of spatial vegetation patterns is a fundamental problem in ecology, especially because these can be used as early predictors of catastrophic shifts such as desertification processes. Empirical studies of…
We study the fluctuations of the area $A=\int_0^T x(t) dt$ under a one-dimensional Brownian motion $x(t)$ in a trapping potential $\sim |x|$, at long times $T\to\infty$. We find that typical fluctuations of $A$ follow a Gaussian…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule,…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving--Kirkwood--Noll procedure. Since the method…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in the high-dimensional regime. We prove limit theorems for the trajectories of summary statistics (i.e., finite-dimensional functions) of SGD as the…