-
作者：O'Brien, GL
作者单位：York University - Canada
摘要：Two classes of processes are considered. One is a class of spectrally positive infinitely divisible processes which includes all such stable processes. The other is a class of processes constructed from the sequence of partial sums of independent identically distributed positive random variables. A condition analogous to regular variation of the tails is imposed. Then a large deviation principle and a Strassen-type law of the iterated logarithm are presented. These theorems focus on unusually ...
-
作者：Marsalle, L
作者单位：Sorbonne Universite
摘要：Let L be a local time. It is well known that there exist a law of the iterated logarithm and a modulus of continuity for L. Motivated by the case of real Brownian motion, we study the existence of fast points and slow points of L. We prove the existence of such points by considering the right-continuous inverse of L, which is a subordinator.
-
作者：Grigorescu, L
作者单位：McMaster University
摘要：We derive explicitly the asymptotic law of the tagged particle process in a system of interacting Brownian motions in the presence of a diffusive scaling in nonequilibrium. The interaction is local and interpolates between the totally independent case (noninteracting) and the totally reflecting case and can be viewed as the limiting local version of an interaction through a pair potential as its support shrinks to zero. We also prove the independence of two tagged particles in the limit.
-
作者：Bentkus, V; Götze, F
作者单位：University of Bielefeld
摘要：Let X, X-1, X-2,... be i.i.d. random variables taking values in a measurable space H. Let phi(x, y) and phi(1)(x) denote measurable functions of the arguments x, y is an element of H. Assuming that the kernel phi is symmetric and that E phi(x, X) = 0, for all x, and E phi(1)(X) = 0, we consider U-statistics of type [GRAPHICS] It is known that the conditions E phi(2)(X, X-1) < infinity and E phi(1)(2)(X) < infinity imply that the distribution function of T, say F, has a limit, say F-0, which ca...
-
作者：DeBlassie, RD
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Let X-t be reflected Brownian motion (RBM) in a cone with radially homogeneous reflection, killed upon reaching the vertex of the cone. We determine the adjoint process and use it to find the Martin boundary of the killed RBM together with all the corresponding positive harmonic functions. Then we can identify and prove uniqueness (up to positive scalar multiples) of the invariant measure for killed RBM and RBM without killing. Along the way, we prove the strong Feller property of the resolven...
-
作者：Chen, X
作者单位：Northwestern University
摘要：Let {X-n}(n greater than or equal to 0) be a Harris recurrent Markov chain with state space (E, E), transition probability P(x, A) and invariant measure pi. Given a nonnegative pi-integrable function f on E, the exact asymptotic order is given for the additive functionals (n)(k=1)Sigma f(X-/e), n=1, 2,... in the forms of both weak and strong convergences. In particular, the frequency of {X-n}(n greater than or equal to 0) visiting a given set A is an element of E with 0 < pi(A) < +infinity is ...
-
作者：Li, WV; Linde, W
作者单位：University of Delaware; Friedrich Schiller University of Jena
摘要：A precise link proved by Kuelbs and Li relates the small ball behavior of a Gaussian measure mu on a Banach space E with the metric entropy behavior of K mu, the unit ball of the reproducing kernel Hilbert space of mu in E. We remove the main regularity assumption imposed on the unknown function in the link. This enables the application of tools and results from functional analysis to small ball problems and leads to small ball estimates of general algebraic type as well as to new estimates fo...
-
作者：Lyons, T; Zeitouni, O
作者单位：Imperial College London; Technion Israel Institute of Technology
摘要：We provide sharp exponential moment bounds for (Stratonovich) iterated stochastic integrals under conditioning by certain small balls, including balls in certain Holder-like norms of exponent greater than 1/3. The proof uses a control of the variation of the Levy area. under conditioning. The results are applied to the computation of the Onsager-Machlup functional of diffusion processes with constant diffusion matrix.
-
作者：Marcus, MB; Rosen, J
作者单位：City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：Different extensions of an isomorphism theorem of Dynkin are developed and are used to study two distinct but related families of functionals of Levy processes; n-fold near-intersections of a single Levy process and continuous additive functionals of several independent Levy processes. Intersection local times for n independent Levy processes are also studied. They are related to both of the above families. In all three cases sufficient conditions are obtained for the almost sure continuity of...
-
作者：Grigorescu, I
作者单位：McMaster University
摘要：It has been shown that for a system of Brownian motions with local interaction considered in a diffusive scaling, under some regularity assumptions on the initial profile, the tagged particle process converges to a diffusion. We provide a sufficient condition for granting both the existence and the uniqueness of the tagged particle process for an arbitrary initial profile.
