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作者：Jain, Naresh; Krylov, Nicolai
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Our aim is to unify and extend the large deviation upper and lower bounds for the occupation times of a Markov process with L-2 semigroups under minimal conditions on the state space and the process trajectories for example, no strong Markov property is needed. The methods used here apply in both continuous and discrete time. We present the proofs for Continuous time only because of the inherent technical difficulties in that situation: the proofs can be adapted for discrete time in a straight...
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作者：Dupuis, Paul; Ishii, Hitoshi
作者单位：Brown University; Waseda University
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作者：Denisov, D.; Dieker, A. B.; Shneer, V.
作者单位：Heriot Watt University; International Business Machines (IBM); IBM USA; Euratom
摘要：For a given one-dimensional random walk {S-n} with a subexponential step-size distribution, we present a unifying theory to study the sequences {x(n)} for which P{S-n > x} as n -> infinity uniformly for x >= x(n). We also investigate the stronger local analogue, P{S-n is an element of (x, x + T]} similar to nP{S-1 is an element of (x, x + T]}. Out- theory is self-contained and fits well within classical results on domains of (partial) attraction and local limit theory. When specialized to the ...
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作者：Kim, Panki; Song, Renming
作者单位：Seoul National University (SNU); University of Illinois System; University of Illinois Urbana-Champaign
摘要：Recently, in [Preprint (2006)], we extended the concept of intrinsic ultra-contractivity to nonsymmetric semigroups. In this paper, we study the intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and measure-valued potentials in bounded domains. Our process Y is a diffusion process whose generator can be formally written as L + mu . del - v with Dirichlet boundary conditions, where L is a uniformly elliptic second-order differential operator and mu = (mu(l)........
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作者：Bernyk, Violetta; Dalang, Robert C.; Peskir, Goran
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Manchester
摘要：Let X = (X-t)(t >= 0) be a stable Levy process of index alpha is an element of (1.2) with no negative jumps and let S-t = sup(0 <= s <= 1) X-s denote its running spremum for t > 0. We show that the density funtion f(1) of S-1 can be characterized as the unique solution to a weakly singular Voleterra integral equation of the first kind or equivalently, as the unique solution to a first-order Riemann-Liouville fractional differential equation satisfying a boundry condition at zero. This yeilds a...
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作者：Bezerra, Sergio; Tindel, Samy; Viens, Frederi
作者单位：Universite de Lorraine; Purdue University System; Purdue University
摘要：This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer ill random medium represented by a Gaussian field W on R+ x R which is white noise in time and function-valued space. According to the behavior of the spatial covariance of W, we give a lower bound on the power growth (wandering exponent) of the polymer when the time parameter goes to infinity: the polymer is proved to be superdiffusive, with a wandering exponent exceeding any alpha < 3/5.
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作者：Kesten, Harry; Sidoravicius, Vladas
作者单位：Cornell University; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We consider the following, problem in one-dimensional diffusion-limited agregation (DLA). At time t, we have an aggregate consisting of Z boolean AND [0, R(t)] [with R(t) a positive integer]. We also have N(i, t) particles at i, i > R(t). All these particle, perform independent continuous-time symmetric simple random Walks until the first time t' > i at Which some particle tries to jump from R(t) + l to R(t). The aggreate is then increased to the integers in [0, R(t')] = [0, R(t) + 1] [so that...
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作者：Pete, Gabor
作者单位：Microsoft
摘要：We consider a four-vertex model introduced by Balint Toth: a dependent bond percolation model on Z(2) in which every edge is present with probability 1/2 and each vertex has exactly two incident edges, perpendicular to each other. We prove that all components are finite cycles almost surely, but the expected diameter of the cycle containing the origin is infinite. Moreover, we derive the following critical exponents; the tail probability P(diameter of the cycle of the origin > n) approximate t...
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作者：Dolgopyat, Dmitry; Keller, Gerhard; Liverani, Carlangelo
作者单位：University System of Maryland; University of Maryland College Park; University of Erlangen Nuremberg; University of Rome Tor Vergata
摘要：We prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving, environment on Z(d). We assume that the transition probabilities of the walk depend not too strongly on the environment and that the evolution of the environment is Markovian with strong spatial and temporal mixing properties.
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作者：Nolin, Pierre
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
摘要：We study gradient percolation for site percolation on the triangular lattice. This is a percolation model where the percolation probability depends linearly on the location of the site. We prove the results predicted by physicists for this model. More precisely, we describe the fluctuations of the interfaces around their (straight) scaling limits, and the expected and typical lengths of these interfaces. These results build on the recent results for critical percolation on this lattice by Smir...
