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作者：PEDDADA, SD; RICHARDS, DSP
摘要：Let m (greater-than-or-equal-to 2) be a positive integer; I(m) be the m x m identity matrix; and SIGMA and A be symmetric m x m matrices, where SIGMA is positive definite. By proving that the function phi-alpha-(A) = \I(m) - 2iA-SIGMA\-alpha is a characteristic function only if alpha element-of {0, 1/2, 1, 3/2, ..., (m - 2)/2} union [(m - 1)/2, infinity), we establish a conjecture of Eaton. A similar result is established for the rank 1 noncentral Wishart distribution and is conjectured to als...
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作者：SHEU, SJ
摘要：In this paper we study the transition density P(t)(x, y) of a nondegenerate diffusion process by using the stochastic control method invented by Fleming and the idea of stochastic parallel translation. We obtain a two-sided estimate for P(t)(x, y) as well as some bounds for the derivatives of log P(t)(x, y).
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作者：CSORGO, S; HAEUSLER, E; MASON, DM
作者单位：University of Delaware; University of Munich
摘要：Let X1,n less-than-or-equal-to ... less-than-or-equal-to X(n, n) be the order statistics of n independent random variables with a common distribution function F and let k(n) be positive integers such that k(n) --> infinity and k(n)/n --> alpha as n --> infinity, where 0 less-than-or-equal-to alpha < 1. We find necessary and sufficient conditions for the existence of normalizing and centering constants A(n) > 0 and C(n) such that the sequence [GRAPHICS] converges in distribution along subsequen...
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作者：LEGALL, JF; ROSEN, J
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：Limit theorems are proved for the range of d-dimensional random walks in the domain of attraction of a stable process of index beta. The range R(n) is the number of distinct sites of Z(d) visited by the random walk before time n. Our results depend on the value of the ratio beta/d. The most interesting results are obtained for 2/3 < beta/d less-than-or-equal-to 1. The law of large numbers then holds for R(n), that is, the sequence R(n)/E(R(n) converges toward some constant and we prove the con...
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作者：CHEN, DC
摘要：A sufficient condition is given for a sequence of partial-sum set-indexed processes with nonuniform phi-mixing condition to converge to Brownian motion. The main result (Theorem 1.1) is an extension of the similar results of Goldie and Greenwood by weakening the phi-mixing condition. An application (Corollary 4.2) to certain Gibbs fields is given.
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作者：CERUTTI, MC; ESCAURIAZA, L; FABES, EB
摘要：We show the well-posedness for the martingale problem associated with a strictly elliptic operator with coefficients bounded and continuous on R(n) except for a countable set having at most one cluster point.
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作者：ROGERS, LCG; WALSH, JB
作者单位：University of British Columbia
摘要：If (B(t))t greater-than-or-equal-to 0 is Brownian motion on R, if A(t,x) = integral-0t(I){B(s) less-than-or-equal-to x} ds and if tau(.,x) is the right-continuous inverse to A(.,x), then the process BBAR(t,x) = B(tau(t,x)) is a reflecting Brownian motion in (-infinity, x]. If E(x) denotes the sigma-field generated by BBAR(.,x), then (E(x))x-element-of-R forms a filtration. It has been proved recently that all (E(x))-martingales are continuous, in common with the martingales on the Brownian fil...
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作者：STEIF, JE
摘要：In this paper, we study spin systems, probabilistic cellular automata and interacting particle systems, which are Markov processes with state space {0, 1}Z(n). Restricting ourselves to attractive systems, we consider the stationary processes obtained when either of two distinguished stationary distributions is used, the smallest and largest stationary distributions with respect to a natural partial order on measures. In discrete time, we show that these stationary processes with state space {0...
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作者：WEINTRAUB, KS
摘要：A random vector is min-stable (or jointly negative exponential) if any weighted minimum of its components has a negative exponential distribution. The vectors can be subordinated to a two-dimensional homogeneous Poisson point process through positive L1 functions called spectral functions. A critical feature of this representation is the point of the Poisson process, called the location, that defines a min-stable random variable. A measure of association between min-stable random variables is ...
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作者：STUTE, W
摘要：We introduce a class of so-called conditional U-statistics, which generalize the Nadaraya-Watson estimate of a regression function in the same way as Hoeffding's classical U-statistic is a generalization of the sample mean. Asymptotic normality and weak and strong consistency are proved.
