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作者：Barbour, AD; Månsson, M
作者单位：University of Zurich; Chalmers University of Technology
摘要：Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are given to illustrate the procedure.
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作者：Bass, RF; Kumagai, T
作者单位：University of Connecticut; Kyoto University
摘要：Let S-n be a random walk in Z(d) and let R-n be the range of Sn. We prove an almost sure invariance principle for R-n when d = 3 and a law of the iterated logarithm for R-n when d = 2.
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作者：Chen, ZQ; Song, RM
作者单位：University of Washington; University of Washington Seattle; University of Illinois System; University of Illinois Urbana-Champaign
摘要：General gauge and conditional gauge theorems are established for a large class of (not necessarily symmetric) strong Markov processes, including Brownian motions with singular drifts and symmetric stable processes. Furthermore, new classes of functions are introduced under which the general gauge and conditional gauge theorems hold. These classes are larger than the classical Kato class when the process is Brownian motion in a bounded C domain.
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作者：Dedecker, J; Merlevède, F
作者单位：Sorbonne Universite
摘要：Following Lindeberg's approach, we obtain a new condition for a stationary sequence of square-integrable and real-valued random variables to satisfy the central limit theorem. In the adapted case, this condition is weaker than any projective criterion derived from Gordin's theorem [Dokl. Akad. Nauk SSSR 188 (1969) 739-741] about approximating martingales. Moreover, our criterion is equivalent to the conditional central limit theorem, which implies stable convergence (in the sense of Renyi) to ...
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作者：Matysiak, W; Szablowski, PJ
作者单位：Warsaw University of Technology
摘要：The aim of this note is to reduce a number of assumptions in the recent paper of W. Bryc by showing that some of them imply the others and to give alternative, simpler proofs of some of Bryc's results.
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作者：Yan, LQ
作者单位：University of British Columbia
摘要：Weak convergence of the Euler scheme for stochastic differential equations is established when coefficients are discontinuous on a set of Lebesgue measure zero. The rate of convergence is presented when coefficients are Holder continuous. Monte Carlo simulations are also discussed.
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作者：Brémont, J
作者单位：Universite de Rennes
摘要：We consider random walks on Z in a stationary random medium, defined by an ergodic dynamical system, in the case when the possible jumps arc {-L,...,-1, 0, + 1} for sonic fixed integer L. We provide a recurrence criterion expressed in terms of the sign of the maximal Liapounov exponent of a certain random matrix and give an algorithm of calculation of that exponent. Next, we characterize the existence of the absolutely continuous invariant measure for the Markov chain of the environments viewe...
