Estimation of the service time distribution in the discrete-time GI/G/∞-queue based solely on information on the arrival and departure processes is considered. The focus is put on the estimation approach via the so called “sequence of differences”. Existing results for this approach are...

Let {Xk:k≥1} be a linear process with values in the separable Hilbert space L2(μ) given by Xk=∑j=0∞(j+1)−Dεk−j for each k≥1, where D is defined by Df={d(s)f(s):s∈S} for each f∈L2(μ) with d:S→R and {εk:k∈Z} are independent and identically distributed L2(μ)-valued random...

Based on an R2-valued random sample {(yi,xi),1≤i≤n} on the simple linear regression model yi=xiβ+α+εi with unknown error variables εi, least squares processes (LSPs) are introduced in D[0,1] for the unknown slope β and intercept α, as well as for the unknown β when α=0. These LSPs...

In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important...

Motivated by its relevance for the study of perturbations of one-dimensional voter models, including stochastic Potts models at low temperature, we consider diffusively rescaled coalescing random walks with branching and killing. Our main result is convergence to a new continuum process, in...

We study two models of population with migration. On an island lives an individual whose genealogy is given by a critical Galton–Watson tree. If its offspring ends up consuming all the resources, any newborn child has to migrate to find new resources. In this sense, the migrations are...

In this paper, we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time Markov chain. The goal is to compute the stationary...

We study the regularity properties of integro-partial differential equations of Hamilton–Jacobi–Bellman type with the terminal condition, which can be interpreted through a stochastic control system, composed of a forward and a backward stochastic differential equation, both driven by a...

The solution Xn to a nonlinear stochastic differential equation of the form dXn(t)+An(t)Xn(t)dt−12∑j=1N(Bjn(t))2Xn(t)dt=∑j=1NBjn(t)Xn(t)dβjn(t)+fn(t)dt, Xn(0)=x, where βjn is a regular approximation of a Brownian motion βj, Bjn(t) is a family of linear continuous operators from V to H...

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the...