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作者：Perera, G; Wschebor, M
作者单位：Universite Paris Saclay; Universidad de la Republica, Uruguay
摘要：We show that 1/root epsilon {integral(-infinity)(infinity) f(u)k(epsilon)N(tau)(X epsilon)(u) du - integral(0)(tau) f(X-t)a(t)dt} converges in law (as a continuous process) to c(psi) f(0)(tau) f(X-t)a(t) dB(t), where X-t = integral(0)(t) a(s) dW(s) + integral(0)(t) b(s) ds, with W a standard Brownian motion, a. and b regular and adapted processes, X-epsilon(t) = integral(-infinity)(infinity)(1/epsilon)psi((t - u)/epsilon)X-u du, psi a smooth kernel, N-t(g)(u) the number of roots of the equatio...
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作者：Leon, JA; Nualart, D
作者单位：Instituto Politecnico Nacional - Mexico; CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; University of Barcelona
摘要：We prove the existence of a unique mild solution for a stochastic evolution equation on a Hilbert space driven by a cylindrical Wiener process. The generator of the corresponding evolution system is supposed to be random and adapted to the filtration generated by the Wiener process. The proof is based on a maximal inequality for the Skorohod integral deduced from the Ito's formula for this anticipating stochastic integral.
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作者：Shi, Z
作者单位：Sorbonne Universite
摘要：We are interested in the almost sure asymptotic behavior of the windings of planar Brownian motion. Both the usual lim sup and Chung's lim inf versions of the law of the iterated logarithm are presented for the so-called big and small winding angles. Our method is based on some very accurate estimates of the winding clock. The corresponding problem for a spherically symmetric random walk in R-2 is also studied. A strong approximation using the Brownian big winding process is established. Simil...
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作者：Le Gall, JF; Le Jan, Y
作者单位：Sorbonne Universite; Universite Paris Saclay
摘要：The main idea of the present work is to associate with a general continuous branching process an exploration process that contains the desirable information about the genealogical structure. The exploration process appears as a simple local time functional of a Levy process with no negative jumps, whose Laplace exponent coincides with the branching mechanism function. This new relation between spectrally positive Levy processes and continuous branching processes provides a unified perspective ...
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作者：Bai, ZD; Silverstein, JW
作者单位：National University of Singapore; North Carolina State University
摘要：Let B-n = (1/N)T-n(1/2) XnXn*T-n(1/2), where X-n is n x N with i.i.d, complex standardized entries having finite fourth moment and T(n)1/2 is a Hermitian square root of the nonnegative definite Hermitian matrix T-n. It is known that, as n --> infinity, if n/N converges to a positive number and the empirical distribution of the eigenvalues of T-n converges to a proper probability distribution, then the empirical distribution of the eigenvalues of B-n converges a.s. to a nonrandom limit. In this...
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作者：Giraitis, L; Taqqu, MS
作者单位：Boston University
摘要：We establish the central limit theorem for quadratic forms Sigma(t, s=1)(N) b(t-s)P-m,P- n(X-t, X-s) of the bivariate Appell polynomials P-m,P- n(X-t, X-s) under time-domain conditions. These conditions relate the weights b(t) and the covariances of the sequences (P-m,P- n(X-t, X-s)) and (X-t). The time-domain approach, together with the spectral domain approach developed earlier, yields a general set of conditions for central limit theorems.
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作者：Uchiyama, K
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：It is shown that an infinite subset of Z(N) is either recurrent for each aperiodic N-dimensional random walk with mean zero and finite variance, or transient for each of such random walks. This is an exact extension of the result by Spitzer in three dimensions to that in the dimensions N greater than or equal to 4.
