Showing papers in "Stochastic Processes and their Applications in 1981"

TL;DR: In this paper, a general stochastic model of a frictionless security market with continuous trading is developed, where the vector price process is given by a semimartingale of a certain class, and the general Stochastic integral is used to represent capital gains.

TL;DR: In this paper, a martingale argument is used to derive the generating function of the number of i.i.d. experiments it takes to observe a given string of outcomes for the first time.

TL;DR: Operator self-similar stochastic processes taking values in a finite dimensional Euclidean space are introduced and some of their properties are studied in this paper, where the authors consider the case where the operator self is a deterministic process.

TL;DR: In this paper, an overjump Markov chain associated with a pair of random walks is used to obtain a sharp estimate of their coupling time; and thence of the convergence rate of a renewal process.

TL;DR: In this article, a survey of the results which have been obtained and some of the open problems, concentrating on six overlapping classes of processes: the voter model, additive processes, the exponential family, one dimensional systems, attractive systems, and the Ising model.

TL;DR: The bounded-dual Lipschitz and Prohorov distances from the empirical measure to the average measure of independent random variables converges to zero almost surely if the sequence of average measures is tight as discussed by the authors.

TL;DR: In this article, it was shown that X ∗ n has a nondegenerate limit distribution if and only if the common probability distribution satisfies a condition of multidimensional regular variation.

TL;DR: In this paper, conditions were obtained for the truncated birth-death process to be stochastically monotone in the long run, which is the same as the conditions obtained in this paper.

TL;DR: In this paper, useful limit results for the standard epidemic model are proved using a martingale central limit theorem given by McLeish, which do not depend on the solutions of the deterministic equations, and also cover the case of a small initial number of infectives.

TL;DR: In this paper, it was shown that if a global solution of the equation dXt = a(Xt) dBt, X0 = x exists for some x ϵ R and ∫∞ 0 a2(Xs)ds = ∞, then one must have a ≠ 0 a.

TL;DR: In this paper, it was shown that any real-valued sequence of random variables {Xn} converging in probability to a non-degenerate, not necessarily a.s.

TL;DR: In this article, it was shown that the multivariate life distributions of Marshall and Shaked actually satisfy the Block-Savits MIFRA condition, and that the damage processes associated with the Marshall-Shaked shock models are multivariate strongly IFRA.

TL;DR: In this article, the authors considered a two firms excess-loss reinsurance problem, where the first firm is defined as the direct underwriter and the second firm is the reinsurer, and they defined an insurance game, solved by employing a Stackelberg solution concept.

TL;DR: In this paper, a new class of stochastic processes, called processes of positive bivariate type, is defined, which is typically one whose bivariate density functions are positive definite, at least for pairs of time points which are sufficiently mutually close.

TL;DR: In this paper, the Strauss clustering model was modified by introducing a hard core component (no two points can have "Xin − Xin" which converges to a positive constant and the boundary of Dn is negligible), which is essentially equivalent to requiring that although the number of points n is large the region is large enough so that the points are sparse in this region.

TL;DR: In this paper, the authors generalized the results on weak convergence to diffusion processes to cases where the limiting diffusions may have regular boundaries and gave two different sets of conditions for convergence.

TL;DR: In this paper, the standard Bernoulli two-armed bandit model is modified by terminating the choice problem after the first unsuccessful trial, and both terminal reward situations and instances in which payoffs accrue with each success are considered.

TL;DR: In this paper, a necessary and sufficient condition for a finite ergodic homogeneous Markov chain to converge to the stationary distribution in a finite number of steps is given, generalizing a recent result of Brosh and Gerchak, who considered only the irreducible case.

TL;DR: In this article, it was shown that Π ∞k = 1 depends upon P(1) and that the limit matrix depends upon the invariant probability matrix associated with P. The convergence rate is determined by the rate of convergence of {P(k) ∞ ∞ k = 1 towards P.

TL;DR: For a continuous time stochastic process with distribution P ϑ depending on a one-dimensional parameter ϑ the problem of sequentially testing ϑ = 0 against ϑ > 0 is treated in this paper.

TL;DR: In this article, conditions under which the partial sums of an array of weakly dependent random variables (X n ) nϵ Z d, d ⩾1, are almost surely asymptotically close to standard Brownian motion are derived.

TL;DR: In this paper, it was shown that, provided the state space of the input process is finite, the limiting distribution of the deficit process of a finite dam tends to the zero-modified distribution above as the capacity tends to infinity.

TL;DR: In this article, it was shown that the mean observed lifetime of a renewal process has a particularly simple form, i.e., it is smaller than the average lifetime of the process mean lifetime.

TL;DR: In this paper, the authors compared trends in the rate of occurence of events for two Poisson series based on a product model which is similar to the one proposed by Cox.

TL;DR: In this paper, the authors show that if b > 1 and if the lower tail of the distribution of Y 1 approaches 0 fast enough, then lim sup n → ∞ (b −1) Σ n j =1 b 1 Y j ⧸ b n + 1 = L, almost certainly, where L is the essential supremum of Y n.

TL;DR: In this paper, it was shown that the asymptotic distribution of the autocorrelations of the resulting residuals coincides with that for least-square residuals, which is similar to the distribution for least square residuals.

TL;DR: In this article, a criticality condition for random environment population processes is derived using a coupling argument, and the criticality parameter governs whether the process dies out or fluctuates about a positive finite constant.

TL;DR: In this paper, confidence intervals for the quantiles of the cumulative mean function of the nonhomogeneous Poisson process are presented, and the problem of selecting quantiles to be used in graphical plotting is considered.