Showing papers in "Stochastic Processes and their Applications in 1990"

TL;DR: In this paper, the effect of dependent errors in fixed-design, nonparametric regression is investigated and it is shown that convergence rates for a regression mean estimator under the assumption of independent errors are maintained in the presence of stationary dependent errors, if and only if Σ r (j ) r is the covariance function.

TL;DR: In this paper, the explicit form of the probability law and the associated flow function of a random motion governed by the telegraph equation are derived and connections of this law with the transition function of Brownian motion are explored.

TL;DR: In this article, a strictly stationary sequence of random variables, where the X's and Y's are R p-valued and R q-valued, respectively, for some integers p, q⩾1.

TL;DR: In this paper, the stability of open Jackson networks is established where service times are i.i.d. general distribution, exogeneous inter-arrival times are I.i., and the routing is Markovian.

TL;DR: In this paper, the authors show that for a stationary (ergodic) sequence of Lipschitz maps of a locally compact Polish space X into itself having a negative Lyapunov exponent function, the composition process Fn⋯F1x converges in distribution to a stationary process in X (independent of x) for every x, the empirical distribution of a trajectory converges with probability one, and for every e>0, almost every trajectory is eventually within e of the support.

TL;DR: In this paper, the central limit theorem with random centering is proved for the empirical vector of the Curie-Weiss-Potts model, which is a model in statistical mechanics.

TL;DR: In this article, the authors derived a good approximation to the characteristic function of Z(n) for the generation dependent version of the process for stable laws, their local analogues and some similar results when a Seneta-Heyde norming is needed.

TL;DR: In this paper, the authors give new central limit theorems and invariance principles for φ-mixing sequences of random variables that support the Ibragimov-Iosifescu conjecture.

TL;DR: In this paper, the authors discuss some aspects of the asymptotic behavior of Discrete Event Dynamic Systems (DEDS), in which the activity times are random variables.

TL;DR: In this paper, the authors show that the partially specified likelihood determines a covariance bound in the sense of a Hajek-LeCam convolution theorem for estimating functionals of the underlying parameter.

TL;DR: In this paper, the limit distributions of multivariate extreme values of stationary random sequences are associated under mild mixing conditions, and sufficient conditions are given such that the limit has independent components.

TL;DR: In this paper, a convergence theory for a class of projected stochastic approximations driven by finite-state Markov chains is developed, and conditions are given explicitly in terms of the model data, mainly the Lipschitz continuity of the one-step transition probabilities.

TL;DR: In this paper, the authors identify the class of stationary processes on an interval which share a given stationary Gaussian process as kth derivative, and the membership requirement involves the norm in the reproducing kernel space associated with the process sought as derivative.

TL;DR: In this paper, necessary and sufficient conditions are given for a symmetric α-stable (SαS) process, 1 < α < 2, to be a Markov process.

TL;DR: In this paper, a family of martingale estimating functions related to the score function is shown to produce convenient simple estimators with good asymptotic efficiency relative to the maximum likelihood estimator.

TL;DR: In this article, the authors considered a free-boundary Ising model X with inverse temperature β > 0 and without external field, and proposed estimators for β and ϵ and shown to be consistent as Λ ≥ Z 2.

TL;DR: In this paper, a stochastic differential delay equation with a small parameter and random noise perturbations is considered, and the martingale averaging techniques are adopted to treat the problem.

TL;DR: In this article, the consistency of regressogram type estimators of the functions T and U was established based on he observation of the process X n + 1 = T ( X n )+ U ( X N ) e n +1, and nonparametric goodness-of-fit tests for the functionsT and U were introduced and discussed.

TL;DR: In this paper, the authors obtained characterization theorems for the possible limits in distribution of a family of stationary random measures satisfying a strong mixing condition, with necessary and sufficient conditions for convergence.

TL;DR: In this paper, a new general approach to constructing a quasi score function for a class of stochastic processes is proposed, where a crucial point in the construction is the separate treatment of the continuous martingale part and the purely discontinuous part.

TL;DR: The results are extended to more general kinds of first passage time problems, so called marked crossings, and used to construct upper and lower bounds for the first passage, wave-length densities and for the transition distribution from a maximum to the following minimum.

TL;DR: Renyi distances which are representing Hellinger integrals and Kullback-Liebler divergences are considered and asymptotic formulas are established for the second kind error of Neyman-Pearson tests, and for the mixed error of Bayes tests.

TL;DR: In this article, the first zero R n of the real part of the empirical characteristic function related to a random variable X has been considered and the limit distribution of R n has been derived.

TL;DR: In this paper, the authors analyze a storage process with dynamical arrivals and departures under probabilistic assumptions, and give the main features of it: the maximal throughput and the occupied length of the unit.

TL;DR: In this article, a class of interacting Ohta-Kimura stepwise-mutation models and their macroscopic behavior is studied and a scaling theorem for these processes is proved.

TL;DR: In this paper, the authors considered a biased voter model in a set of all subsets of Z, where the recovery rates, δ x, x ∈ Z, are iid random variables and λ>0 is fixed.

TL;DR: In this paper, a law of large numbers theorem for measure-valued processes describing the age distribution of particles is established based on Hilbertian techniques, as the measures are regarded as elements of the dual of some weighted Sobolev space.

TL;DR: In this article, the sufficient conditions under which the first equation is still exponentially stable almost surely are discussed, and sufficient conditions for the second equation to be exponentially stable at the same time are discussed.

TL;DR: In this paper, the weak invariance theorem of generalized U-statistic for non-stationary regular variables was established for the stationary case and extended to the nonstationary case.

TL;DR: In this article, the authors formulated the stepping-stone model in population genetics as a measure-valued diffusion process and proved an ergodic property of the process corresponding to the solution of the martingale problem under a suitable assumption on the mechanism of mutation.