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作者：Müller-Gronbach, T
作者单位：Otto von Guericke University
摘要：We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a measurable way) on a finite number of sequential observations of the driving Brownian motion. The resulting lower error bounds hold in particular for all methods that are implementable on a computer and use a random number generator to simulate the driving Brownian m...
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作者：Balister, P; Bollobás, B; Walters, M
作者单位：University of Memphis
摘要：Let A be the annulus in R-2 centered at the origin with inner and outer radii r(1 - epsilon) and r, respectively. Place points {x(i)} in R-2 according to a Poisson process with intensity 1 and let G(A) be the random graph with vertex set {x(i)} and edges x(i)x(j) whenever x(i) - x(j) is an element of A. We show that if the area of A is large, then G(A) almost surely has an infinite component. Moreover, if we fix epsilon, increase r and let n(c) = n(c)(epsilon) be the area of A when this infini...
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作者：Kroese, DP; Scheinhardt, WRW; Taylor, PG
作者单位：University of Queensland; University of Twente; Centrum Wiskunde & Informatica (CWI); University of Melbourne
摘要：Quasi-birth-and-death (QBD) processes with infinite phase spaces can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the phase giving the state of the first queue and the level giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of News's R-matrix and show that the decay rate of the station...
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作者：Albin, JMP
作者单位：Chalmers University of Technology
摘要：Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(epsilon)(-1) at which a stochastic process with stationary increments should be sampled, for the sampled process xi([(.)/q(epsilon)]q(epsilon)) to deviate from xi by at most epsilon, with a given probability, asymptotically as epsilon down arrow 0. The canonical application is to discretization errors in computer simulation of stochastic processes.
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作者：Chi, ZY
作者单位：University of Chicago
摘要：We consider the asymptotics of various estimators based on a large sample of branching trees from a critical multi-type Galton-Watson process, as the sample size increases to infinity. The asymptotics of additive functions of trees, such as sizes of trees and frequencies of types within trees, a higher-order asymptotic of the relative frequency estimator of the left eigenvector of the mean matrix, a higher-order joint asymptotic of the maximum likelihood estimators of the offspring probabiliti...
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作者：Klüppelberg, C; Kyprianou, AE; Maller, RA
作者单位：Technical University of Munich; Utrecht University; Australian National University; Australian National University
摘要：We formulate the insurance risk process in a general Levy process setting, and give general theorems for the ruin probability and the asymptotic distribution of the overshoot of the process above a high level, when the process drifts to -infinity a.s. and the positive tail of the Levy measure, or of the ladder height measure, is subexponential or, more generally, convolution equivalent. Results of Asmussen and Kluppelberg [Stochastic Process. Appl. 64 (1996) 103-125] and Bertoin and Doney [Adv...
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作者：Silvestrov, DS; Teugels, JL
作者单位：Malardalen University; KU Leuven
摘要：This article is devoted to the investigation of limit theorems for mixed max-sum processes with renewal type stopping indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems.
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作者：Bhattacharya, R; Majumdar, M
作者单位：Indiana University System; Indiana University Bloomington; Cornell University
摘要：Iteration of randomly chosen quadratic maps defines a Markov process: Xn+1 = epsilon(n+1) X-n(1 - X-n), where epsilon(n) are i.i.d. with values in the parameter space [0, 4] of quadratic maps F-theta(x) = thetax(1 - x). Its study is of significance as an important Markov model, with applications to problems of optimization under uncertainty arising in economics. In this article a broad criterion is established for positive Harris recurrence of X-n.
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作者：Dalang, RC; Hongler, MO
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider the problem of finding the optimal time to sell a stock, subject to a fixed sales cost and an exponential discounting rate P. We assume that the price of the stock fluctuates according to the equation dY(t) = Y-t(mudt + sigmaxi(t)dt), where (xi(t)) is an alternating Markov renewal process with values in {+/-1}, with an exponential renewal time. We determine the critical value of p under which the value function is finite. We examine the validity of the principle of smooth fit and u...
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作者：Goldstein, L
作者单位：University of Southern California
摘要：Given F: [a,b](k) --> [a,b] and a nonconstant X-0 with P(X-0 is an element of [a,b]) = 1, define the hierarchical sequence of random variables {X-n}(ngreater than or equal to0) by Xn+1 = F(X-n,X-1,...,X-n,X-k), where X-n,X-i are i.i.d. as X-n. Such sequences arise from hierarchical structures which have been extensively studied in the physics literature to model, for example, the conductivity of a random medium. Under an averaging and smoothness condition on nontrivial F, an upper bound of the...
