Showing papers in "Stochastic Processes and their Applications in 1978"

TL;DR: A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form X N (t)=x 0 + ∑ 1 N lY 1 N ∫ t 0 f 1 (X N (s))ds where l ∈ Z t, the Y 1 are independent Poisson processes, and N is a parameter with a natural interpretation.

TL;DR: In this paper, the authors considered a branching diffusion where particles move during their life time according to a Brownian motion with drift -μ and variance coefficient σ 2, and in which each particle which enters the negative half line is instantaneously removed from the population.

TL;DR: The infinite divisibility of generalized inverse Gaussian distributions with non-positive power parameters was shown in this paper, where the first hitting time of level 0 for each of a variety of time-homogeneous diffusions on the interval [0, ∞] was shown.

TL;DR: In this article, a storage system whose content fluctuates as a Brownian Motion is considered, and the problem is to minimize expected discounted cost subject to the requirement that X ( t ) + Y( t ) - Z ( t ), t ) ⩾ 0 for all t ≥ 0 almost surely.

TL;DR: In this paper, the authors describe the asymptotic distribution of such processes and show how it arises in limits of certain functionals of these processes and give a partial answer to an anomaly in the classical economic lot size inventory model.

TL;DR: In this paper, a generalized definition of invertibility is proposed and applied to linear, non-linear and bilinear models and it is shown that some recently studied nonlinear models are not invertible, but conditions for invertability can be achieved for the other models.

TL;DR: In this paper, a time-indexed representation for a sequence of self-similar processes Z m (t), m=1,2,…, whose finite-dimensional moments have been specified in an earlier paper, is presented.

TL;DR: In this paper, a generalization for the stochastic integrals associated with a two-parameter Wiener process is presented, where the objective is to represent a suitably differentiable function f(Xz) as such a sum once again.

TL;DR: In this paper, the problem of finding an optimal control policy that minimizes the total long run average cost per unit of time is addressed. But the authors assume that the accumulated damage is observable and that the hazard rate associated with the random variable V is monotonically nondecreasing, and they show that the optimal policy is a control limit policy.

TL;DR: In this article, the authors consider some parametric spectral estimators that can be used in a wide range of situations and establish rates of convergence of the estimators, and a central limit theorem.

TL;DR: In this article, the authors obtained results concerning the distribution of generations and degree of relationship of the individuals in a critical branching process and applied these results to obtain a central limit theorem for critical branching random walks.

TL;DR: In this article, a random time change is defined as a map from one function space to another, and the continuity of this map is investigated, and applications are made to weak limit theorems of random processes.

TL;DR: In this article, the exact modulus of non-differentiability of a Wiener Process has been shown to be the same as the modulus for continuity of a WPA.

TL;DR: In this paper, the authors considered the problem of optimal stopping for a sequence of independent, identically distributed r.v. with a continuous distribution function, and proved that optimal stopping rules for all problems exist.

TL;DR: In this article, the inventory control in a class of M/G/1 queueing systems is discussed. But the authors focus on the problem of inventory control with two switchover levels.

TL;DR: In this paper, the maximum likelihood estimator is shown to be the best consistent asymptotically normal estimator in the sense of having minimum variance, and it also produces the best limiting probability of concentration in symmetric intervals.

TL;DR: In this article, it was shown that the asymptotic distribution of the maximum Mn =max1= 0 as t -> ~ or if Σr2t<~, then the limiting distribution is the same as for a sequence of independent normal variables.

TL;DR: In this paper, a probabilistic characterization of strongly excessive Markov decision processes is presented in the form of a random drift through a partitioned state space, and a characterization in terms of the spectral radius of the process is given.

TL;DR: In this paper, the mean and autocovariance function of the product sequence of two stationary time series x t and y t is derived, where x t is the product of two time series.

TL;DR: In this article, the spectral radius of P − Q is used to characterize the eigenvalues of P and determine the geometric rate at which P n converges to Q in case P is strongly ergodic.

TL;DR: In this article, a functional central limit theorem is obtained for martingales which are not uniformly asymptotically negligible but grow at a geometric rate, and as simple corollaries the already known central limit theorems for the Harris and Lotka-Nagaev estimators of the mean of the offspring distribution are obtained.

TL;DR: In this paper, the problem of finding a suitable (asymptotic) efficiency criterion for inference concerning parameters of stochastic processes is addressed, and a contiguity calculation is used to show that a previously suggested criterion is inadequate and itself provides a partial solution to the problem.

TL;DR: In this article, a subset of stochastically monotone Markov chains has the property that the expectation of unimodal functions of the chain is itself unimodally in the initial state.

TL;DR: In this article, simple conditions are given which characterize the generating function of a nonnegative multivariate infinitely divisible random vector, and sufficient conditions on marginals, linear combinations, tail behavior, and zeroes are discussed.

TL;DR: In this paper, nonparametric estimators for discrete time nonhomogeneous Markov chains are derived using the maximum likelihood principle, and asymptotic unbiasedness and strong consistency of the estimators are proved.

TL;DR: In this article, the structure of a nonlinear filter with observation process having continuous and discontinuous components is considered and the approach is based on the so-called "Bayes" formula for conditional expectations.

TL;DR: In this paper, the authors consider a simple problem in the optimal control of Brownian motion and show that there exists an optimal policy involving just two critical numbers, and formulas are given for computation of the critical numbers.

TL;DR: In this article, the authors consider large classes of continuous time optimal stopping problems for which they establish the existence and form of the optimal stopping times, which are then used to find approximate optimal solutions for a class of discrete time problems.

TL;DR: In this paper, sufficient conditions are established for approximation of the overflow probability in a stochastic service system with capacity C by the probability that the related infinite-capacity system has C customers.

TL;DR: In this article, it was shown that the distribution of the ratio of two independent gamma-distributed random variables is infinitely divisible, which was the first result in the theory of infinite divisibility.