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作者：BRADLEY, RC
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：For strictly stationary random fields indexed by R(d) or Z(d), certain versions of the ''strong mixing'' condition are equivalent to corresponding versions of the ''p-mixing'' condition.
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作者：BOLTHAUSEN, E; DEUSCHEL, JD
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We investigate large deviations for the empirical distribution functional of a Gaussian random field on R(Zd), d greater than or equal to 3, in the phase transition regime. We first prove that the specific entropy governs an N-d volume order large deviation principle outside the Gibbsian class. Within the Gibbsian class we derive an N-d-2 capacity order large deviation principle with exact rate function, and we apply this result to the asymptotics of microcanonical ensembles. We also give a sp...
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作者：FREIDLIN, MI; WENTZELL, AD
摘要：A number of asymptotic problems for ''classical'' stochastic processes leads to diffusion processes on graphs. In this paper we study several such examples and develop a general technique for these problems. Diffusion in narrow tubes, processes with fast transmutations and small random perturbations of Hamiltonian systems are studied.
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作者：SLUD, EV
摘要：Let Y be a random variable defined by a polynomial p(W) of degree n in finitely many normally distributed variables. This paper studies which such variables Y are ''determinate,'' i.e., have probability laws uniquely determined by their moments. Extending results of Berg, which applied to powers of a single normal variable, we prove that (a) Y is determinate if n = 1, 2 or if n = 4, with the essential support of the law of Y strictly smaller than the real line, and (b) Y is not determinate eit...
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作者：ENCHEV, O
摘要：We study shift transformations on a general abstract Wiener space (E, H, mu), which have the form: E contains omega --> T(phi)omega equivalent to omega - integral(0)(T) phi(t)(omega)Z(dt) is an element of E, where phi(t)(omega) is a scalar function on [0,T] x E and Z is an orthogonal H-valued measure. Under suitable conditions for the kernel phi, we construct explicitly a probability measure mu(phi) on E, which is equivalent to the standard Wiener measure mu and has the property: mu(phi){T-phi...
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作者：LALLEY, SP
摘要：Local limit theorems and saddlepoint approximations are given for random walks on a free group whose step distributions have finite support. The techniques used to prove these results are necessarily different from those used for random walks in Euclidean spaces, because Fourier analysis is not available; the basic tools are the elementary theory of algebraic functions and the Perron-Frobenius theory of nonnegative matrices. An application to the structure of the boundary process is also given.
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作者：PRAESTGAARD, J; WELLNER, JA
作者单位：University of Washington; University of Washington Seattle
摘要：We consider an exchangeably weighted bootstrap of the general function-indexed empirical process. We find sufficient conditions on the bootstrap weights for the central limit theorem to hold for the bootstrapped empirical process, almost surely and in probability. The results resemble those of Gine and Zinn for Efron's bootstrap. As a corollary we obtain a result on the almost sure convergence in distribution of the Efron-bootstrapped empirical process with arbitrary sample size. A large numbe...
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作者：BRAMSON, M; COX, JT; GREVEN, A
作者单位：Syracuse University; University of Gottingen
摘要：We consider two critical spatial branching processes on R(d): critical branching Brownian motion, and the Dawson-Watanabe process. A basic feature of these processes is that their ergodic behavior is highly dimension-dependent. It is known that in low dimensions, d less than or equal to 2, the unique invariant measure with finite intensity is delta(0), the unit point mass on the empty state. In high dimensions, d greater than or equal to 3, there is a one-parameter family of nondegenerate inva...
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作者：BURTON, RM; GOULET, M; MEESTER, R
作者单位：Utrecht University
摘要：A stationary process {X(n)}(n epsilon Z) is said to be k-dependent if {X(n)}(n<0) is independent of {X(n)}(n>k-1). It is said to be a k-block factor of a process {Y-n} if it can be represented as X(n) = f(Y-n,...,Y-n+k-1), where f is a measurable function of k variables. Any (k + 1)-block factor of an i.i.d. process is k-dependent. We answer an old question by showing that there exists a one-dependent process which is not a k-block factor of any i.i.d. process for any k. Our method also leads ...
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作者：ZHANG, Y
摘要：Cox and Durrett proved the shape theorem of epidemics and forest fires with nearest neighbor interactions. They also conjectured that the shape theorem is still true with finite range interactions. In this paper, we answer this conjecture affirmatively. The method we develop allows us also to improve the result of Zhang and Zhang for all dimension.
