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作者：Nourdin, Ivan; Rosinski, Jan
作者单位：Universite de Lorraine; University of Tennessee System; University of Tennessee Knoxville
摘要：We characterize the asymptotic independence between blocks consisting of multiple Wiener-Ito integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati, its multidimensional extension and other related results on the multivariate convergence of multiple Wiener-Ito integrals, that involve Gaussian and non Gaussian limits. We give applications to the study of the asymptotic behavior of functions of short and long-range dependent st...
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作者：Cerrai, Sandra; Da Prato, Giuseppe
作者单位：University System of Maryland; University of Maryland College Park; Scuola Normale Superiore di Pisa
摘要：We consider the Kolmogorov operator associated with a reaction diffusion equation having polynomially growing reaction coefficient and perturbed by a noise of multiplicative type, in the Banach space E of continuous functions. By analyzing the smoothing properties of the associated transition semigroup, we prove a modification of the classical identite du carre des champs that applies to the present non-Hilbertian setting. As an application of this identity, we construct the Sobolev space W-1,...
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作者：Handa, Kenji
作者单位：Saga University
摘要：We identify stationary distributions of generalized Fleming-Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a Dirichlet random measure with the same parameter measure. The calculations are based primarily on the well-known relationship to measure-valued branching processes with immigration.
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作者：Goetze, Friedrich; Zaitsev, Andrei Yu
作者单位：University of Bielefeld; Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：Let X, X-1, X-2,... be i.i.d. R-d-valued real random vectors. Assume that EX = 0, cov X = C, E vertical bar vertical bar X vertical bar vertical bar(2) = sigma(2) and that X is not concentrated in a proper subspace of R-d Let G be a mean zero Gaussian random vector with the same covariance operator as that of X. We study the distributions of nondegenerate quadratic forms Q[S-N] of the normalized sums S-N = N-(1/2) (X-1 +...+ X-N) and show that, without any additional conditions, Delta(N) =(def...
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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(...
