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作者：Wang, FY
作者单位：Beijing Normal University
摘要：By using probabilistic approaches, some uniform gradient estimates are obtained for Dirichlet heat semigroups on a Riemannian manifold with boundary. As an application, lower bound estimates of isoperimetric constants are presented in terms of functional inequalities.
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作者：Attal, SP; Lindsay, JM
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Nottingham
摘要：Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic integrals are all defined simply in terms of the orthogonal projections of the time filtration of Fock space, together with sections of the adapted gradient operator. Free from exponential vector domains, our stochastic integrals may be satisfactorily composed yielding quantum Ito formulas for ope...
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作者：Mathieu, P; Remy, E
作者单位：Aix-Marseille Universite
摘要：We prove that the heat kernel on the infinite Bernoulli percolation cluster in Z(d) almost surely decays faster than t(-d/2). We also derive estimates on the mixing time for the random walk confined to a finite box. Our approach is based on local isoperimetric inequalities. Some of the results of this paper were previously announced in the note of Mathieu and Remy.
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作者：Bai, ZD; Silverstein, JW
作者单位：Northeast Normal University - China; North Carolina State University; National University of Singapore
摘要：Let B-n = (1/N)T-n(1/2) XnX*T-n(n)1/2 where X-n = (X-ij) is n x N with i.i.d. complex standardized entries having finite fourth moment, and T-n(1/2) is a Hermitian square root of the nonnegative definite Hermitian matrix T-n. The limiting behavior, as n --> infinity with n/N approaching a positive constant, of functionals of the eigenvalues of B-n, where each is given equal weight, is studied. Due to the limiting behavior of the empirical spectral distribution of B,,, it is known that these li...
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作者：Abadi, M
作者单位：Universidade de Sao Paulo
摘要：We prove an upper bound for the error in the exponential approximation of the hitting time law of a rare event in alpha-mixing processes with exponential decay, phi-mixing processes with a summable function phi and for general psi-mixing processes with a finite alphabet. In the first case the bound is uniform as a function of the measure of the event. In the last two cases the bound depends also on the time scale t. This allows us to get further statistical properties as the ratio convergence ...
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作者：Chistyakov, GP; Götze, F
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
摘要：Let X, X-j, j is an element of N, be independent, identically distributed random variables with probability distribution F. It is shown that Student's statistic of the sample {X-j}(n)(j=1), has a limit distribution G such that G({-1, 1}) not equal 1, if and only if: (1) X is in the domain of attraction of a stable law with some exponent 0 < alpha less than or equal to 2; (2) EX = 0 if 1 < alpha < 2; (3) if alpha = 1, then X is in the domain of attraction of Cauchy's law and Feller's condition ...
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作者：Berti, P; Rigo, P
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：A notion of convergence in distribution for non (necessarily) measurable random elements, due to Hoffmann-Jorgensen, is characterized in terms of weak convergence of finitely additive probability measures. A similar characterization is given for a strengthened version of such a notion. Further, it is shown that the empirical process for an exchangeable sequence can fail to converge, due to the nonexistence of any measurable limit, although it converges for an i.i.d. sequence. Because of phenom...
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作者：Martínez, S; Martín, JS
作者单位：Universidad de Chile
摘要：We show necessary and sufficient conditions for R-recurrence and R-positivity of one-dimensional diffusions killed at the origin. These conditions are stated in terms of the bottom eigenvalue function.
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作者：Pyke, R; Van Zwet, WR
作者单位：University of Washington; University of Washington Seattle; Leiden University; Leiden University - Excl LUMC
摘要：This paper obtains the weak convergence of the empirical processes of both the division points and the spacings that result from the Kakutani interval splitting model. In both cases, the limit processes are Gaussian. For the division points themselves, the empirical processes converge to a Brownian bridge as they do for the usual uniform splitting model, but with the striking difference that its standard deviations are about one-half as large. This result gives a clear measure of the degree of...
