-
作者：SZULGA, J
摘要：Multiple stochastic integrals with respect to an infinitely divisible symmetric random measure are constructed for integrands taking values in a Banach space.
-
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...
-
作者：GOROSTIZA, LG; WAKOLBINGER, A
作者单位：Johannes Kepler University Linz
摘要：We consider a system of particles in R(d) performing symmetric stable motion with exponent alpha, 0 < alpha less-than-or-equal-to 2, and branching at the end of an exponential lifetime with offspring generating function F(s) = s + 1/2(1 - s)1+beta, 0 < beta less-than-or-equal-to 1. (This includes binary branching Brownian motion for alpha = 2, beta = 1.) It is shown that, for an initial Poisson population with uniform intensity, the system goes to extinction if d less-than-or-equal-to alpha/be...
-
作者：KWAPIEN, S; SZULGA, J
作者单位：Auburn University System; Auburn University
摘要：We prove that if (theta-k) is a sequence of i.i.d. real random variables then, for 1 < q < p, the linear combinations of (theta-k) have comparable pth and qth moments if and only if the joint distribution of (theta-k) is (p, q)-hypercontractive. We elaborate hypercontraction methods in a new proof of the inequality. [GRAPHICS] where (X(i)) is a sequence of independent zero-mean random variables with values in a normed space, and C(p) almost-equal-to p/ln p.
-
作者：JACKA, SD
摘要：This paper establishes the best constant c(q) appearing in inequalities of the form [GRAPHICS] where M is an arbitrary nonnegative submartingale and [GRAPHICS] The method of proof is via the Lagrangian for a version of the problem [GRAPHICS] where M = \B\, B a Brownian motion. More general inequalities of the form [GRAPHICS] and [GRAPHICS] (where parallel-to . parallel-to-phi and phi are, respectively, the Luxemburg norm and its dual, the Orlicz norm, associated with a Young function PHI) are ...
-
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...
-
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.
-
作者：ADLER, RJ; FELDMAN, RE; LEWIN, M
作者单位：University of California System; University of California Berkeley; University of California System; University of California Santa Barbara
摘要：The Brownian density process is a distribution-valued process that arises either via a limiting operation on an infinite collection of Brownian motions or as the solution of a stochastic partial differential equation. It has a (self-) intersection local time, that is formally defined through an operation involving delta functions, much akin to the better studied intersection local time of measure-valued (super) processes. Our main aim is to show that this formal definition not only makes sense...
-
作者：GRIFFIN, P; KUELBS, J
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We study some generalizations of the LIL when self-normalizations are used. Two particular results proved are: (1) an extension of the Kolmogorov-Erdos test for partial sums of symmetric i.i.d. random variables having finite second moments; this result eliminates distinctions required when nonrandom normalizers are used and E(X2I(\X\ > t)) is not O((L2t)-1), and (2) an extension of a universal bounded LIL of Marcinkiewicz to nonsymmetric random variables. An interesting corollary of this work ...
-
作者：MAITRA, A; PURVES, R; SUDDERTH, W
作者单位：University of California System; University of California Berkeley
摘要：Starting at x in a Polish space X, a player selects the distribution sigma-0 of the next state x1 from the collection GAMMA(x) of those distributions available and then selects the distribution sigma-1(x1) for x2 from GAMMA(x1) and so on. Suppose the player wins if every x(i) in the stochastic process x1, x2,... lies in a given Borel subset A of X, that is, if the process stays in A forever. If {(x, gamma): gamma epsilon GAMMA(x)} is a Borel subset of X x P(X), where P(X) is the natural Polish...
