-
作者：Khoshnevisan, D; Xiao, YM
作者单位：Utah System of Higher Education; University of Utah; Michigan State University
摘要：We use the recently-developed multiparameter theory of additive Levy processes to establish novel connections between an arbitrary Levy process X in R-d, and a new class of energy forms and their corresponding capacities. We then apply these connections to solve two long-standing problems in the folklore of the theory of Levy processes. First, we compute the Hausdorff dimension of the image X(G) of a nonrandorn linear Borel set G subset of R+, where X is all arbitrary Levy process in Rd. Our w...
-
作者：Gnedin, A; Pitman, J
作者单位：Utrecht University; University of California System; University of California Berkeley
摘要：A new class of random composition structures (the ordered analog of Kingman's partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random sampling of points from an exponential distribution on the positive halfline, and separating the points into clusters by an independent regenerative random set. Examples are composition structures derived from residual allocation models, including one associa...
-
作者：Klenke, A; Mörters, P
作者单位：Johannes Gutenberg University of Mainz; University of Bath
摘要：Let f be the projected intersection local time of two independent Brownian paths in R-d for d = 2, 3. We determine the lower tail of the random variable l(U), where U is the unit ball. The answer is given in terms of intersection exponents, which are explicitly known in the case of planar Brownian motion. We use this result to obtain the multifractal spectrum, or spectrum of thin points, for the intersection local times.
-
作者：Hairer, M
作者单位：University of Warwick
摘要：We study the ergodic properties of finite-dimensional systems of SDEs driven by nondegenerate additive fractional Brownian motion with arbitrary Hurst parameter H is an element of (0, 1). A general framework is constructed to make precise the notions of invariant measure and stationary state for such a system. We then prove under rather weak dissipativity conditions that such an SIDE possesses a unique stationary solution and that the convergence rate of an arbitrary solution toward the statio...
-
作者：Haydn, N; Lacroix, Y; Vaienti, S
作者单位：University of Southern California; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite
摘要：Given an ergodic dynamical system (X, T, mu), and U subset of X measurable with mu(U) > 0, let mu(U)tau(U)(x) denote the normalized hitting time of x is an element of X to U. We prove that given a sequence (U-n) with mu(U-n) -> 0, the distribution function of the normalized hitting times to U-n converges weakly to some subprobability distribution F if and only if the distribution function of the normalized return time converges weakly to some distribution function and that in the converging ca...
-
作者：Xia, C
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：Let S-1 (n), . . ., S-p(n) be independent symmetric random walks in Z(d). We establish moderate deviations and law of the iterated logarithm for the intersection of the ranges #{S-1[0, n] boolean AND . . . boolean AND S-p[0, n]} in the case d = 2, p >= 2 and the case d = 3, p = 2.
-
作者：Schramm, O; Sheffield, S
作者单位：Microsoft; University of California System; University of California Berkeley
摘要：The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left-hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE4 as the grid gets finer.
-
作者：Dubédat, J
作者单位：Universite Paris Saclay
摘要：Various features of the two-parameter family of Schramm-Loewner evolutions SLE(kappa, rho) are studied. In particular, we derive certain restriction properties that lead to a strong duality conjecture, which is an identity in law between the outer boundary of a variant of the SLE(kappa) process for kappa greater than or equal to 4 and a variant of the SLE(16/kappa) process.
