Showing papers in "Stochastic Processes and their Applications in 1988"

TL;DR: In this article, it was shown that stationary vector ARMA processes are geometrically completely regular and hence geometrical strong mixing, provided the innovations have a continuous distribution with respect to Lebesgue measure.

TL;DR: In this paper, it was shown that the spatial epidemic with removal grows linearly and has an asymptotic shape on the set of nonextinction, which is the same as the one described in this paper.

TL;DR: In this paper, the authors developed several results in the modern theory of contingent claims valuation in a frictionless security market with continuous trading, where the price model is a semi-martingale with a certain structure, making the return of the security a sum of an Ito process and a random, marked point process.

TL;DR: Asymptotic approximations for surface integrals for stationary differentiable Gaussian vector processes are derived and the expected number of crossings through a hypersurface is given.

TL;DR: In this article, it was shown that a point process based on the moving average process converges weakly, and a host of complementary results concerning extremal properties of {Xn} can then be derived from this convergence result.

TL;DR: In this article, the estimation of the spectral measure of a stationary process is considered and an equicontinuity condition and a weak convergence result for the resulting spectral process are proved.

TL;DR: In this paper, a sharp martingale comparison method is introduced which results in a necessary and sufficient condition for W to be non-degenerate in the Galton-Watson process.

TL;DR: In this paper, the authors define the least squares estimator ϴ n,τ and show that under some regularity conditions, ϴn,τ is strongly consistent under the Gaussian assumption.

TL;DR: In this article, a simple procedure is proposed for estimating the coefficients from observations of the linear process X1=∑xJ=0ψJZ1−j, 1=1,2.

TL;DR: Theorem 1 of Welsch (1972) is generalized in this article, and some links between the convergence of the order statistics and that of certain point processes are established, where natural interpretations can be given for the p j.

TL;DR: In this paper, two disjoint classes of self similar symmetric stable processes with stationary increments are studied and the domain of attraction of the harmonizable fractional stable processes is discussed.

TL;DR: In this paper, a scaling limit theorem for critical spatially homogeneous branching processes of finite intensity is given in terms of scaling limit, provided that the dimension of the ambient space is small enough.

TL;DR: In this article, a weighted least squares estimator is used to estimate the hazard functions in Aalen's additive risk model from grouped (and possibly censored) survival data, and counting process techniques are applied to derive a functional central limit theorem for the integrated estimator.

TL;DR: The Central Bureau of Statistics as mentioned in this paper have published a discussion paper on the impact of nettressurs on the distribution of net-tressurings in the world of statistics.

TL;DR: In this article, a Berry-Esseen theorem and a functional law of the Iterated Logarithm are obtained for d-dimensional random vectors. But the present paper does not consider the functional central limit theorem.

TL;DR: In this paper, the authors approximate the empirical process, based on multivariate random samples with an arbitrary distribution function, by a single Gaussian process, using a Gaussian Process.

TL;DR: An embedding of an arbitrary centred law μ in a Brownian motion (that is a stopping time T and a motion B such that L (B t )= μ and ( B tΛT ; t ⩾0) is found such that B ∗ T has a law which dominates that of M ∗ τ, where the pair (M, τ ) is any other ui embedding as mentioned in this paper.

TL;DR: The strong link between optimal selection and optimal stopping of record sequences or record processes, perhaps not fully recognized so far, is pointed out in this paper, which leads to a unification of the treatment of problems which, at first sight, are rather different.

TL;DR: In this paper, the authors studied the finite horizon Bellman equation for controlled Markov jump models with unbounded jump and cost rates and proved the existence of a solution, and constructed a computationally attractive approximation scheme.

TL;DR: In this paper, the first problem of answering whether all 1/α-self-similar α-stable processes with stationary increments are α-stable motions was studied, and the answer was yes for α = 2, no for 1⩽α.

TL;DR: In this paper, a locally interacting particle system is studied which can be interpreted as a stochastic model of a chemical reaction with diffusion, and a central limit theorem for the empirical distribution, using an asymptotic expansion of correlation functions, is established.

TL;DR: In this article, the authors study the asymptotic behavior of the distribution function of the order statistics from a stable sample and give necessary conditions for a.s. boundedness of general stable processes.

TL;DR: In this article, the authors consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points, and they show how admissibility can be related directly to observable characteristics of the investment strategy.

TL;DR: In this paper, sufficient conditions for pure jump Markov processes Xt to have local times that serve as occupation time densities are given for the stable-like case and α(x) Dini continuous.

TL;DR: In this article, the authors considered a Markov chain with transition densities whose state space is a Euclidian space and showed that it is reversible with respect to some density, and time-reversible or not.

TL;DR: In this paper, the secretary problem for a random walk is described and the optimal strategy of picking the maximum height in n steps without the opportunity of recall is found, which is exactly the same as the naive strategy of choosing the first element of the sequence.

TL;DR: In this article, a generalization of the decreasing failure rate (DFR) concept is introduced, based on the following principle: if there have been many points of occurrence recently, then we will soon experience another one.

TL;DR: In this article, it was shown that the limit distribution of the partial maxima of a multivariate Gaussian sequence is equal to the product of the marginal limit distributions of the M ni's or to the asymptotic product of X k's under certain conditions.

TL;DR: In this paper, the Feynman propagator in a uniform magnetic field can be explicitly computed in terms of P. Levy's stochastic area spanned by two-dimensional Brownian motion.

TL;DR: In this paper, a nonlinear least squares estimator for the model is derived and shown to be strongly consistent and asymptotically normally distributed under the assumption of normality, an iterative procedure is suggested to obtain maximum likelihood estimates of the model.