Related papers: On discrete-time self-similar processes with stati…
This paper introduces a discrete-time fractional Poisson process defined as a renewal process, where the waiting times follow a discrete Mittag-Leffler distribution. We investigate its fundamental properties by explicitly deriving the…
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
We present here an elementary example, for every fixed positive integer $k,$ of a strictly stationary nongaussian stochastic process in discrete time, all of whose $k$-marginals are gaussian.
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet. This Gaussian field is an extension of fractional Brownian motion. We prove some properties of covariance function for self-similar fields…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
Understanding the influence of activity on dense amorphous assemblies is crucial for biological processes such as wound healing, embryogenesis, or cancer progression. Here, we study the effect of self-propulsion forces of amplitude $f_0$…
The steady state reached by a system of particles sliding down a fluctuating surface has interesting properties. Particle clusters form and break rapidly, leading to a broad distribution of sizes and large fluctuations. The density-density…
We discuss the non-uniqueness of continuous solutions to differential equations with a {\it discrete } state-dependent delay and continuous initial functions. We are interested not only in the fact (conditions) of non-uniqueness, but in…
We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for…
Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanism for point processes. Here, we are interested in their domains of attraction and…
In this paper we study solutions to multivariate stochastic delay differential equations (MSDDEs) which have stationary increments, and we show that this modeling framework is in many ways similar to the discrete-time cointegrated VAR…
We present a dimension-incremental method for function approximation in bounded orthonormal product bases to learn the solutions of various differential equations. Therefore, we decompose the source function of the differential equation…
We introduce the wavelet scattering spectra which provide non-Gaussian models of time-series having stationary increments. A complex wavelet transform computes signal variations at each scale. Dependencies across scales are captured by the…
Our purpose is to investigate properties for processes with stationary and independent increments under $G$-expectation. As applications, we prove the martingale characterization to $G$-Brownian motion and present a decomposition for…
Point-gap topology, characterized by spectral winding numbers, is crucial to non-Hermitian topological phases and dramatically alters real-time dynamics. In this paper, we study the evolution of quantum particles in dissipative systems with…
In this paper, we show that the exponential integrator scheme both in spatial discretization and time discretization for a class of stochastic partial differential equations has a unique stationary distribution whenever the stepsize is…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider a fundamental…