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作者：INGLOT, T; KALLENBERG, WCM; LEDWINA, T
作者单位：University of Twente
摘要：Strong moderate deviation theorems are concerned with relative errors in the tails caused by replacing the exact distribution function by its limiting distribution function. A new approach for deriving such theorems is presented using strong approximation inequalities. In this way a strong moderate deviation theorem is obtained for statistics of the form T(alpha(n)), where T is a sublinear functional and alpha(n) is the empirical process. The basic theorem is also applied on linear combination...
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作者：LAWLER, GF; BRAMSON, M; GRIFFEATH, D
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We study the asymptotic shape of the occupied region for an interacting lattice system proposed recently by Diaconis and Fulton. In this model particles are repeatedly dropped at the origin of the d-dimensional integers. Each successive particle then performs an independent simple random walk until it sticks at the first site not previously occupied. Our main theorem asserts that as the cluster of stuck particles grows, its shape approaches a Euclidean ball. The proof of this result involves G...
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作者：PENROSE, MD
摘要：We define a semi-min-stable (SMS) process Y(t) in [0, infinity) to be one which is stable under the simultaneous operations of taking the minima of n independent copies of Y(t) (pointwise over time t) and rescaling space and time. We show that the only possible rescaling of time is by a fixed power of n and that SMS processes are essentially the only possible weak limits for large m of a process obtained by taking the minimum, pointwise over t, of m independent copies of a given process and th...
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作者：LEE, TY
摘要：A branching diffusion process is studied when its diffusivity decreases to 0 at the rate of E much less than 1 and its branching/transmutation intensity increases at the rate of epsilon--1. We derive the action functionals which describe some large deviations of the processes as epsilon tends to 0. The branching diffusion processes are closely related to systems of semilinear parabolic differential equations.
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作者：SHEPP, LA; ZEITOUNI, O
作者单位：Technion Israel Institute of Technology
摘要：It is proven that, for any deterministic L2[0, 1] function phi(t), E(exp integral-1/0-phi(t)dw(t)\parallel-to w parallel-to < epsilon) --> 1 as epsilon --> 0, where w(t) is a standard Brownian motion and parallel-to . parallel to is any reasonable norm on C0[0, 1]. Applications to the computation of Onsager-Machlup functionals are pointed out.
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作者：ELTON, J; HILL, TP
摘要：Starting with a Borel probability measure P on X (where X is a separable Banach space or a compact metrizable convex subset of a locally convex topological vector space), the class F(P), called the fusions of P, consists of all Borel probability measures on X which can be obtained from P by fusing parts of the mass of P, that is, by collapsing parts of the mass of P to their respective barycenters. The class F(P) is shown to be convex, and the ordering induced on the space of all Borel probabi...
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作者：ROSEN, J
摘要：In this paper we develop an asymptotic expansion for the epsilon-neighborhood of the symmetric stable process of order beta, 1 < beta < 2. Our expansion is in powers of epsilon-2-beta with the nth coefficient related to n-fold self-intersections of our stable process.
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作者：CHEN, LHY; CHOI, KP
摘要：Let X(n1),...,X(nn), n greater-than-or-equal-to 1, be independent random variables with P(X(ni) = 1) = 1 - P(X(ni) = 0) = p(ni) such that max{p(ni): 1 less-than-or-equal-to i less-than-or-equal-to n} --> 0 as n --> infinity. Let W(n) = SIGMA1 less-than-or-equal-to k less-than-or-equal-to n X(nk) and let Z be a Poisson random variable with mean lambda = EW(n). Poisson approximation for the distribution of W(n) dates back to 1960, when Le Cam obtained upper bounds for the total variation distanc...
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作者：ALSMEYER, G
摘要：Let X1, X2,... be i.i.d. random variables with common mean mu greater-than-or-equal-to 0 and associated random walk S0 = 0, S(n) = X1 + ... + X(n), n greater-than-or-equal-to 1. For a regularly varying function phi(t) = t(alpha)L(t), alpha > -1 with slowly varying L(t), we consider the generalized renewal function U(phi)(t) = SIGMA(n greater-than-or-equal-to 0) phi(n)P(S(n) less-than-or-equal-to t), t is-an-element-of R, by relating it to the family tau = tau(t) = inf{n greater-than-or-equal-t...
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作者：FLEMING, WH; JAMES, MR
作者单位：University of Kentucky
摘要：This paper is concerned with accurate asymptotic estimates for exit time probabilities associated with nearly deterministic Markov diffusions. The exit time probabilities are expressed as asymptotic series of WKB type in a small parameter, which measures the strength of the random Brownian motion inputs. This series is valid in certain regions in which the minimum action function u(x, s) is a smooth function of state x and time s. The function u is a solution to the cor-responding Hamilton-Jac...
