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作者：Chen, DY; Peres, Y; Pete, G
作者单位：Peking University; University of California System; University of California Berkeley
摘要：Benjamini, Lyons and Schramm [Random Walks and Discrete Potential Theory (1999) 56-84] considered properties of an infinite graph G, and the simple random walk on it, that are preserved by random perturbations. In this paper we solve several problems raised by those authors. The anchored expansion constant is a variant of the Cheeger constant; its positivity implies positive lower speed for the simple random walk, as shown by Virag [Geom. Funct. Anal. 10 (2000) 1588-1605]. We prove that if G h...
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作者：Berti, P; Rigo, P
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：A notion of convergence in distribution for non (necessarily) measurable random elements, due to Hoffmann-Jorgensen, is characterized in terms of weak convergence of finitely additive probability measures. A similar characterization is given for a strengthened version of such a notion. Further, it is shown that the empirical process for an exchangeable sequence can fail to converge, due to the nonexistence of any measurable limit, although it converges for an i.i.d. sequence. Because of phenom...
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作者：Cerrai, S; Röckner, M
作者单位：University of Florence; University of Bielefeld
摘要：Following classical work by Freidlin [Trans. Amer Math. Soc. (1988) 305 665-657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504-537] and Peszat [Probab. Theory Related Fields (1994) 98 113-136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction-diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, assuming the reaction terms to be only locally Lipschitz with polynomial growth. This generalizes results...
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作者：Chen, ZQ; Fitzsimmons, PJ; Takeda, M; Ying, J; Zhang, TS
作者单位：University of Washington; University of Washington Seattle; Tohoku University; University of California System; University of California San Diego; Fudan University; University of Manchester
摘要：We study Girsanov's theorem in the context of symmetric Markov processes, extending earlier work of Fukushima-Takeda and Fitzsimmons on Girsanov transformations of gradient type. We investigate the most general Girsanov transformation leading to another symmetric Markov process. This investigation requires an extension of the forward-backward martingale method of Lyons-Zheng, to cover the case of processes with jumps.
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作者：Funaki, T
作者单位：University of Tokyo
摘要：We study the zero temperature limit for interacting Brownian particles in one dimension with a pairwise potential which is of finite range and attains a unique minimum when the distance of two particles becomes a > 0. We say a chain is formed when the particles are arranged in an almost equal distance a. If a chain is formed at time 0, so is for positive time as the temperature of the system decreases to 0 and, under a suitable macroscopic space-time scaling, the center of mass of the chain pe...
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作者：Martínez, S; Martín, JS
作者单位：Universidad de Chile
摘要：We show necessary and sufficient conditions for R-recurrence and R-positivity of one-dimensional diffusions killed at the origin. These conditions are stated in terms of the bottom eigenvalue function.
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作者：Pyke, R; Van Zwet, WR
作者单位：University of Washington; University of Washington Seattle; Leiden University; Leiden University - Excl LUMC
摘要：This paper obtains the weak convergence of the empirical processes of both the division points and the spacings that result from the Kakutani interval splitting model. In both cases, the limit processes are Gaussian. For the division points themselves, the empirical processes converge to a Brownian bridge as they do for the usual uniform splitting model, but with the striking difference that its standard deviations are about one-half as large. This result gives a clear measure of the degree of...
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作者：De Acosta, A
作者单位：University System of Ohio; Case Western Reserve University
摘要：We refine the conditions for the lower bound in an abstract large deviation result with nonconvex rate function we had previously introduced. We apply the results to certain stochastic recursive schemes.
