-
作者：Bhattacharya, R
作者单位：Indiana University System; Indiana University Bloomington
摘要：Consider diffusions on R-k, k > 1, governed by the It (o) over cap equation dX(t) = {b(X(t)) + beta(X(t)/a)} dt + sigma dB(t), where b, beta are periodic with the same period and are divergence free, cr is nonsingular and a is a large integer. Two distinct Gaussian phases occur as time progresses. The initial phase is exhibited over times 1 much less than t much less than a(2/3). Under a geometric condition on the velocity field beta, the final Gaussian phase occurs for times t much greater th...
-
作者：Milstein, GN; Tretyakov, MV
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Ural Federal University
摘要：Mean-square approximations, which ensure boundedness of both time and space increments, are constructed for stochastic differential equations in a bounded domain. The proposed algorithms are based on a space-time discretization using a random walk over boundaries of small space-time parallelepipeds. To realize the algorithms, exact distributions for exit points of the space-time Brownian motion from a space-time parallelepiped are given. Convergence theorems are stated for the proposed algorit...
-
作者：Cox, JT; Schinazi, RB
作者单位：Syracuse University; University of Colorado System; University of Colorado at Colorado Springs
摘要：We consider a gene with two alleles. Allele A is normal, allele S is abnormal. Individuals with genotype SS have a severe disease called sickle-cell disease. Individuals with genotype AS are not sick, and it is thought that they are more resistant to malarial infection than individuals with genotype AA. This could explain why the allele S has persisted in regions where malaria is endemic. We use a stochastic spatial process to test this hypothesis. For our model, we show that if the genotype A...
-
作者：Horváth, L; Shao, QM
作者单位：Utah System of Higher Education; University of Utah; University of Oregon
摘要：We establish strong and weak approximations for quadratic forms of weakly and strongly dependent random variables and obtain necessary and sufficient conditions for the weak convergence of weighted functions of quadratic forms. The results are applied to get the asymptotic distributions of some tests which can be used to detect possible changes in the long-memory parameter.
-
作者：Jones, BD; Pittel, BG; Verducci, JS
作者单位：University System of Ohio; Kenyon College; University System of Ohio; Ohio State University; University System of Ohio; Ohio State University
摘要：For a complete graph K-n on n vertices with weighted edges, define the weight of a spanning tree (more generally, spanning forest) as the product of edge weights involved. Define the tree weight (forest weight) of K-n as the total weight of all spanning trees (forests). The uniform edge weight distribution is shown to maximize the tree weight, and an explicit bound on the tree weight is formulated in terms of the overall variance of edge weights as well as the variance of the sum of edge weigh...
-
作者：Stein, ML
作者单位：University of Chicago
摘要：This work investigates some spectral characteristics of the errors of optimal linear predictors for weakly stationary random fields. More specifically, for errors of optimal linear predictors, results here explicitly bound the fraction of the variance attributable to some set of frequencies. Such a bound is first obtained for random fields on R-d observed on the infinite lattice delta J for all J on the d-dimensional integer lattice. If the spectral density exists, then the faster the spectral...
-
作者：Resnick, S; Samorodnitsky, G; Xue, F
作者单位：Cornell University; Cornell University
摘要：For the stable moving average process X-t = integral(-infinity)(infinity) f(t + x) M(dx), t= 1,2,...., we find the weak limit of its sample autocorrelation function as the sample size n increases to infinity. It turns out that, as a rule, this limit is random! This shows how dangerous it is to rely on sample correlation as a model fitting tool in the heavy tailed case. We discuss for what functions f this limit is nonrandom for all (or only some-this can be the case, too!) lags.
-
作者：Bättig, R
作者单位：Cornell University
摘要：We propose a notion of market completeness which is invariant under change to an equivalent probability measure. Completeness means that an operator T acting on stopping time simple trading strategies has dense range in the weak* topology on bounded random variables. In our setup, the claims which can be approximated by attainable ones has codimension equal to the dimension of the kernel of the adjoint operator T* acting on signed measures, which in most cases is equal to the dimension of the ...
-
作者：Durrett, R
-
作者：Madras, N; Piccioni, M
作者单位：York University - Canada; University of L'Aquila
摘要：This paper analyzes the performance of importance sampling distributions for computing expectations with respect to a whole family of probability laws in the context of Markov chain Monte Carlo simulation methods. Motivations for such a study arise in statistics as well as in statistical physics. Two choices of importance sampling distributions are considered in detail: mixtures of the distributions of interest and distributions that are uniform over energy levels (motivated by physical applic...
