Related papers: Stationary, Markov, stochastic processes with poly…
We present a diffusion model of surface soil pollution from a stationary source based on the symmetric stochastic motion at finite speed in the plane $\Bbb R^2$, also called the planar Markov random flight, whose lifetime is a random…
In this paper some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias…
The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…
We consider a one-dimensional stationary stochastic process $x(\tau)$ of duration $T$. We study the probability density function (PDF) $P(t_{\rm m}|T)$ of the time $t_{\rm m}$ at which $x(\tau)$ reaches its global maximum. By using a path…
The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a…
Consider a stochastic process $\{X(t)\}$ on a finite state space $ {\sf X}=\{1,\dots, d\}$. It is conditionally Markov, given a real-valued `input process' $\{\zeta(t)\}$. This is assumed to be small, which is modeled through the scaling,…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
The aim of the paper is to understand how the inclusion of more and more time-scales into a stochastic stationary Markovian process affects its conditional probability. To this end, we consider two Gaussian processes: (i) a short-range…
Piecewise-deterministic Markov processes (PDMPs) are often used to model abrupt changes in the global environment or capabilities of a controlled system. This is typically done by considering a set of "operating modes" (each with its own…
We explore the dynamics of active elements performing persistent random motion with fluctuating active speed and in the presence of translational noise in a $d$-dimensional harmonic trap, modeling active speed generation through an…
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…
We study the long-time behavior of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical properties of the surviving sample attain…
Imagine you walk in a plane. You move by making a step of a certain length per time interval in a chosen direction. Repeating this process by randomly sampling step length and turning angle defines a two-dimensional random walk in what we…
The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such…
We consider a stochastic spatial point process with births and deaths on $\mathbb{R}^d$, with the hard-core property that at any time the balls of radius half of any two points do not overlap. We give explicit construction of the process.…
Random processes with stationary increments and intrinsic random processes are two concepts commonly used to deal with non-stationary random processes. They are broader classes than stationary random processes and conceptually closely…
This paper motivates the use of random-bridges -- stochastic processes conditioned to take target distributions at fixed timepoints -- in the realm of generative modelling. Herein, random-bridges can act as stochastic transports between two…
We consider a one-dimensional stationary time series of fixed duration $T$. We investigate the time $t_{\rm m}$ at which the process reaches the global maximum within the time interval $[0,T]$. By using a path-decomposition technique, we…
This paper investigates the stochastic permanence of malaria and the existence of a stationary distribution for the stochastic process describing the disease dynamics over sufficiently longtime. The malaria system is highly random with…
A method for the construction of approximate analytical expressions for the stationary marginal densities of general stochastic search processes is proposed. By the marginal densities, regions of the search space that with high probability…