-
作者：RIO, E
摘要：This paper contains some extension of Kolmogorov's maximal inequality to dependent sequences. Next we derive dependent Marcinkiewicz-Zygmund type strong laws of large numbers from this inequality. In particular, for stationary strongly mixing sequences (X(i))(i) (is an element of) (Z) with sequence of mixing coefficients (alpha(n))(n greater than or equal to 0), the Marcinkiewicz-Zygmund SLLN of order p holds if integral(0)(1)[alpha(-1)(t)](p-1)Q(p)(t) dt < infinity, where alpha(-1) denotes th...
-
作者：DAVIS, RA; HSING, TL
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Let {xi(j)} be a strictly stationary sequence of random variables with regularly varying tail probabilities. We consider, via point process methods, weak convergence of the partial sums, S-n = xi(1) + ... + xi(n), suitably normalized, when {xi(j)} satisfies a mild mixing condition. We first give a characterization of the limit point processes for the sequence of point processes N-n with mass at the points {xi(j)/a(n), j = 1,..., n}, where a(n) is the 1 - n(-1) quantile of the distribution of \...
-
作者：SHAO, QM
摘要：A Rosenthal-type inequality for maximum partial sums of rho-mixing sequences is obtained. Applications to the complete convergence and almost sure summability of partial sums are also discussed.
-
作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：Consider 0 < alpha < 1 and the Gaussian process Y(t) on R(N) with covariance E(Y(t)Y(s)) = \t\(2 alpha) + \s\(2 alpha) - \t - s\(2 alpha), where \t\ is the Euclidean norm of t. Consider independent copies X(1),...,X(d) Of Y and the process X(t) = (X(1)(t),...,X(d)(t)) valued in R(d). In the transient case (N < alpha d) we show that a.s. for each compact set L of R(N) with nonempty interior, we have 0 < mu(phi)(X(L)) < infinity, where mu(phi), denotes the Hausdorff measure associated with the f...
-
作者：WANG, JG
摘要：Let M be a locally square integrable martingale with predictable quadratic Variance (M) and let Delta M = M - M_ be the jump process of M. In this paper, under the Various restrictions on Delta M, the different increasing rates of M in terms of (M) are obtained. For stochastic integrals X = B . M of the predictable process B with respect to M, the a.s. asymptotic behavior of X is also discussed under restrictions on the rates of increase of B and the restrictions on the conditional distributio...
-
作者：HSING, TL
摘要：It is shown that Sigma(i=1)(n) X(n) and max(i=1)(n)X(i) are asymptotically independent if {X(i)} is strongly mixing and Sigma(i=1)(n)X(i) is asymptotically Gaussian. This generalizes a result of Anderson and Turkman.
-
作者：ADLER, RJ; SAMORODNITSKY, G
作者单位：Cornell University
摘要：We consider the full weak convergence, in appropriate function spaces, of systems of noninteracting particles undergoing critical branching and following a self-similar spatial motion with stationary increments. The limit processes are measure-valued, and are of the super and historical process type. In the case in which the underlying motion is that of a fractional Brownian motion, we obtain a characterization of the limit process as a kind of stochastic integral against the historical proces...
-
作者：KHOSHNEVISAN, D
摘要：Let W be a real-valued, two-parameter Brownian sheet. Let us define N(t; h) to be the total number of bubbles of W in [0, t](2), whose maximum height is greater than h. Evidently, lim(h down arrow 0) N(t; h) = infinity and lim(t) (up arrow) (infinity) N(t; h) = infinity. It is the goal of this paper to provide fairly accurate estimates on N(t; h) both as t --> infinity and as h --> 0. Loosely speaking, we show that there are of order h(-3) many such bubbles as h down arrow 0 and t(3) many, as ...
-
作者：QUASTEL, J
摘要：The hydrodynamic limit appears as a law of large numbers for rescaled density profiles of a large stochastic system. We study the large deviations from this scaling limit for a particular nongradient system, the nongradient version of the Ginzburg-Landau model.
-
作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：Consider a mean zero random variable X, and an independent sequence (X(n)) distributed like X. We show that the random Fourier series Sigma(n greater than or equal to 1) n(-1)X(n) exp(2i pi nt) converges uniformly almost surely if and only if E(\X\ log log(max(e(e), \X\))) < infinity.
