-
作者：Chen, ZQ; Durrett, R; Ma, G
作者单位：Cornell University
摘要：We study a family of differential operators (L-alpha, alpha greater than or equal to 0) in the unit bah D of C-n with n greater than or equal to 2 that generalize the classical Laplacian, alpha = 0, and the conformal Laplacian, alpha = 1/2 (that is, the Laplace-Beltrami operator for Bergman metric in D). Using the diffusion processes associated with these (degenerate) differential operators, the boundary behavior of L-alpha-harmonic functions is studied in a unified way for 0 less than or equa...
-
作者：Mohammed, SEA; Scheutzow, MKR
作者单位：Southern Illinois University System; Southern Illinois University; Technical University of Berlin
摘要：we give several examples and examine case studies of linear stochastic functional differential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semiflow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate <(lambda)over bar>(1) (sigma) of the trajectories expressed in terms of the noise variance sigma. Roughly speaking we show that for small sigma, <(lambda)over bar>(...
-
作者：Choi, KP; Klass, MJ
作者单位：National University of Singapore; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Let Phi(.) be a nondecreasing convex function on [0, infinity). We show that for any integer n greater than or equal to 1 and real a, E Phi((M-n - a)(+)) less than or equal to 2E Phi((S-n - a)(+)) - Phi(0) and E(M-n boolean OR med S-n) less than or equal to E\S-n - med S-n\. where X-1, X-2,... are any independent mean zero random variables with partial sums S-0 = 0, S-k = X-1 +...+ X-k and partial sum maxima M-n = max(0 less than or equal to k less than or equal to n) S-k. There are various in...
-
作者：van der Hofstad, R; den Hollander, F; König, W
作者单位：Utrecht University; Radboud University Nijmegen; Technical University of Berlin
摘要：The Edwards model in one dimension is a transformed path measure for standard Brownian motion discouraging self-intersections. We prove a central limit theorem for the endpoint of the path, extending a law of large numbers proved by Westwater. The scaled variance is characterized in terms of the largest eigenvalue of a one-parameter family of differential operators, introduced and analyzed by van der Hofstad and den Hollander. Interestingly, the scaled variance turns out to be independent of t...
-
作者：Liggett, TM
作者单位：University of California System; University of California Los Angeles
摘要：Interacting particle systems is by now a mature area of probability theory, but one that is still very active. We begin this paper by explaining how models from this area arise in fields such as physics and biology. We turn then to a discussion of both older and more recent results about them, concentrating on contact processes, voter models, and exclusion processes. These processes are among the most studied in the field, and have the virtue of relative simplicity in their description, which ...
-
作者：Donati-Martin, C; Yor, M
作者单位：Sorbonne Universite
摘要：We develop some topics about Brownian motion with a particular emphasis on the study of principal values of Brownian local times. We show some links between principal values and Doob's h-transforms of Brownian motion, for nonpositive harmonic functions h. We also give a survey and complement some martingale approaches to Ray-Knight theorems for local times.
-
作者：Latala, R
作者单位：University of Warsaw
摘要：For the sum S = Sigma X-i of a sequence (X-i) of independent symmetric (or nonnegative) random variables, we give lower and upper estimates of moments of S. The estimates are exact, up to some universal constants, and extend the previous results for particular types of variables X-i.
-
作者：Takeda, M; Zhang, TS
作者单位：University of Osaka; University of Bielefeld
摘要：In this paper we study the asymptotic behavior of additive functionals of Brownian motion which are not necessarily of bounded variation. The result is then applied to the Hilbert transform of the Brownian local time.
-
作者：Fitzsimmons, PJ
作者单位：University of California System; University of California San Diego
摘要：Let X and Y be symmetric diffusion processes with a common state space, and let P-m (resp. Q(mu)) be the law of X (resp. Y) with its symmetry measure m (resp. mu) as initial distribution. We study the consequences of the absolute continuity condition Q(mu) much less than loc P-m. We show that under this condition there is a smooth version rho of the Radon-Nikodym derivative d(mu)/dm such that 1/2[log rho(X-t) - log rho(X-0)] = M-t + N-t, t < sigma, where M is a continuous local martingale addi...
-
作者：Peligrad, M; Utev, S
作者单位：University System of Ohio; University of Cincinnati; La Trobe University; Russian Academy of Sciences
摘要：In this paper we study the CLT for partial sums of a generalized linear process X-n = Sigma(i=1)(n) a(ni)xi(i), where sup(n) Sigma(i=1)(n) a(ni)(2) < infinity, max(1 less than or equal to i less than or equal to n)\a(ni)\ --> 0 as n --> infinity and xi(i)'s are in turn, pairwise mixing martingale differences, mixing sequences or associated sequences. The results are important in analyzing the asymptotical properties of some estimators as well as of linear processes.
