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作者：Hu, Yaozhong; Nualart, David; Xu, Fangjun
作者单位：University of Kansas; East China Normal University
摘要：We prove a central limit theorem for an additive functional of the d-dimensional fractional Brownian motion with Hurst index H is an element of (1/1+d, 1/d), using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.
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作者：Borodin, Alexei; Corwin, Ivan; Sasamoto, Tomohiro
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Columbia University; Chiba University
摘要：We prove duality relations for two interacting particle systems: the q-deformed totally asymmetric simple exclusion process (q-TASEP) and the asymmetric simple exclusion process (ASEP). Expectations of the duality functionals correspond to certain joint moments of particle locations or integrated currents, respectively. Duality implies that they solve systems of ODEs. These systems are integrable and for particular step and half-stationary initial data we use a nested contour integral ansatz t...
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作者：Tong, Xin Thomson; van Handel, Ramon
作者单位：New York University; Princeton University
摘要：The goal of this paper is to develop a general method to establish conditional ergodicity of infinite-dimensional Markov chains. Given a Markov chain in a product space, we aim to understand the ergodic properties of its conditional distributions given one of the components. Such questions play a fundamental role in the ergodic theory of nonlinear filters. In the setting of Harris chains, conditional ergodicity has been established under general nondegeneracy assumptions. Unfortunately, Markov...
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作者：Nguyen, Hoi H.; Van Vu
作者单位：University System of Ohio; Ohio State University; Yale University
摘要：Let A(n) be an n by n random matrix whose entries are independent real random variables with mean zero, variance one and with subexponential tail. We show that the logarithm of vertical bar det A(n)vertical bar I satisfies a central limit theorem. More precisely, [GRAPHICS] .
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作者：Knowles, Antti; Yin, Jun
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We derive the joint asymptotic distribution of the outlier eigenvalues of an additively deformed Wigner matrix H. Our only assumptions on the deformation are that its rank be fixed and its norm bounded. Our results extend those of [The isotropic semicircle law and deformation of Wigner matrices. Preprint] by admitting overlapping outliers and by computing the joint distribution of all outliers. In particular, we give a complete description of the failure of universality first observed in [Ann....
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作者：Zhang, Xicheng
作者单位：Wuhan University
摘要：In this work, by using the Malliavin calculus, under Hormander's condition, we prove the existence of distributional densities for the solutions of stochastic differential equations driven by degenerate subordinated Brownian motions. Moreover, in a special degenerate case, we also obtain the smoothness of the density. In particular, we obtain the existence of smooth heat kernels for the following fractional kinetic Fokker Planck (nonlocal) operator: L-b((alpha)) := Delta(alpha/2)(v) + v . del(...
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作者：Berkes, Istvan; Liu, Weidong; Wu, Wei Biao
作者单位：Graz University of Technology; Shanghai Jiao Tong University; University of Chicago
摘要：The celebrated results of Komlos, Major and Tusnady [Z. Wahrsch. Verw. Gebiete 32 (1975) 111-131; Z. Wahrsch. Verw. Gebiete 34 (1976) 33-58] give optimal Wiener approximation for the partial sums of i.i.d. random variables and provide a powerful tool in probability and statistics. In this paper we extend KMT approximation for a large class of dependent stationary processes, solving a long standing open problem in probability theory. Under the framework of stationary causal processes and functi...
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作者：Dirksen, Sjoerd
作者单位：University of Bonn
摘要：Motivated by the study of existence, uniqueness and regularity of solutions to stochastic partial differential equations driven by jump noise, we prove Ito isomorphisms for L-p-valued stochastic integrals with respect to a compensated Poisson random measure. The principal ingredients for the proof are novel Rosenthal type inequalities for independent random variables taking values in a (noncommutative) L-p-space, which may be of independent interest. As a by-product of our proof, we observe so...
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作者：Crane, Harry
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a sigma-finite measure on stochastic matrices and a collection of nonnegative real constants. This decomposition prompts a Levy-Ito representation. In discrete-time, the evolution is described more simply by a product of independent, identically distributed random matrices.
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作者：Adler, Robert J.; Moldavskaya, Elina; Samorodnitsky, Gennady
作者单位：Technion Israel Institute of Technology; Cornell University
摘要：The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or not two or more points which lie in an excursion set belong to the same connected component has constantly eluded analysis. We study this problem from the point of view of large deviations, finding the asymptotic probabilities that two such points are connected by a path laying within the excursion set, and so belong...
