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作者：Davis, B
摘要：Let alpha and beta be real numbers and f is an element of C-0[O,infinity). We study the existence and uniqueness of solutions g of the equation g(t) =f(t)f alpha sup(0 less than or equal to s less than or equal to) t g(s) + beta info 0 (less than or equal to s less than or equal to) t g(S). Carmona, Petit, Le Gall, and Yor have shown existence (or noxexistence) and uniqueness for some alpha, beta. We settle the remaining cases. We study the nearest neighbor walk on the integers, which behaves ...
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作者：Lotov, VI
摘要：We consider random walks with Gaussian distribution of summands. New representations for Wiener-Kopf factorization components are obtained. The factorization method is used to study the distribution of the excess over one-sided and two-sided boundaries. asymptotic expansions for these distributions and for the expectation of the first exit time are obtained under the assumption that the boundaries tend to infinity.
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作者：Collamore, JF
摘要：Let {Y-n}(n is an element of Z+) be a sequence of random variables in R(d) and let A subset of R(d). Then P{Y-n is an element of A for some n} is the hitting probability of the set A by the sequence {Y-n}. We consider the asymptotic behavior, as m --> infinity, of P{Y-n is an element of mA, some n} = P{hitting mA} whenever (1) the probability law of Y-n/n satisfies the large deviation principle and (2) the central tendency of Y-n/n is directed away from the given set A. For a particular functi...
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作者：Landim, C; Olla, S; Yau, HT
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; New York University
摘要：The hydrodynamical limit of asymmetric simple exclusion processes is given by an inviscid Burgers equation and its next-order correction is given by the viscous Burgers equation. The diffusivity can be characterized by an abstract formulation in a Hilbert space with the inverse of the diffusivity characterized by a variational formula. Alternatively, it can be described by the Green-Kubo formula. We give arguments that these two formulations are equivalent. We also derive two other variational...
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作者：Mytnik, L
摘要：We study the limiting behavior of large branching particle systems undergoing random motion, whose branching mechanism is affected by a random environment. The weak convergence result is established for a sequence of such particle systems and the limiting process is characterized as the unique solution of a martingale problem. The proof of uniqueness of the solution for the martingale problem requires an extension of standard duality techniques.
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作者：Thorisson, H
摘要：Consider a locally compact second countable topological transformation group acting measurably on an arbitrary space. We show that the distributions of two random elements X and X' in this space agree on invariant sets if and only if there is a random transformation Gamma such that Gamma X has the same distribution as X'. Applying this to random fields in d dimensions under site shifts, we show further that these equivalent claims are also equivalent to site-average total variation convergence...
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作者：Jakubowski, A
摘要：We generalize existing Limit theory for stochastic integrals driven by semimartingales and with left-continuous integrands. Joint Skorohod convergence is replaced with joint finite dimensional convergence plus an assumption excluding the case when oscillations of the integrand appear immediately before oscillations of the integrator. Integrands may converge in a very weak topology It is also proved that convergence of integrators implies convergence of stochastic integrals with respect to the ...
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作者：Sethuraman, S; Xu, L
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We give easily verifiable conditions under which a functional central limit theorem holds for additive functionals of symmetric simple exclusion and symmetric zero-range processes. Also a reversible exclusion model with speed change is considered. Let eta(t) be the configuration of the process at time t and let f(eta) be a function on the state space. The question is: For which functions f does lambda(-1/2)integral(0)(M) f(eta(s)) ds converge to a Brownian motion? A general but often intractab...
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作者：Gentz, B
摘要：We consider the Hopfield model with n neurons and an increasing number p = p(n) of randomly chosen patterns. Under the condition (p(3) log p)/n --> 0, we prove for every fixed choice of overlap parameters a central limit theorem as n --> infinity, which holds for almost all realizations of the random patterns. in the special case where the temperature is above the critical one and there is no external magnetic field, the condition (p(2) log p)/n --> 0 suffices. As in the case of a finite numbe...
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作者：Lyons, R; Pemantle, R; Peres, Y
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
摘要：Kaimanovich and Vershik described certain finitely generated groups of exponential growth such that simple random walk on their Cayley graph escapes from the identity at a sublinear rate, or equivalently, all bounded harmonic functions on the Cayley graph are constant. Here we focus on a key example, called G(1) by Kaimanovich and Vershik, and show that inward-biased random walks on G(1) move outward faster than simple random walk. Indeed, they escape from the identity at a linear rate provide...
