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Journals and Conferences
Using the method of transportation-information inequality introduced in , we establish Bernstein type’s concentration inequalities for empirical means 1 t ∫ t 0 g(Xs)ds where g is a unbounded observable of the symmetric Markov process (Xt). Three approaches are proposed : functional inequalities approach ; Lyapunov function method ; and an approach… (More)
DEVIATION INEQUALITIES AND MODERATE DEVIATIONS FOR ESTIMATORS OF PARAMETERS IN AN ORNSTEIN-UHLENBECK PROCESS WITH LINEAR DRIFT FUQING GAO School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R.China email: firstname.lastname@example.org HUI JIANG School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China email:… (More)
Poisson-Dirichlet distribution arises in many different areas. The parameter θ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting procedure of θ approaching infinity is practically motivated and has led to new interesting mathematical structures. Results of law of large numbers, fluctuation… (More)
We consider the comparison theorem of one-dimensional stochastic differential equation with non-Lipschitz diffusion coefficient. Considering the two one-dimensional stochastic differential equations as a two-dimensional equation, we present a necessary condition such that comparison theorem holds by viscosity solution approach.
We study the number of k-cycles in a random graph G(n, p). We estimate the probability that a random graph contains more k-cycles than expected. In this case, the usual martingale inequality with bounded difference is not effective. By constructing a variable that approximates to the number of k-cycles in a random graph and using a new and extensive… (More)
We study the asymptotics for the statistic of chi-square in type II error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.
The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and Gamma subordinators with the two-parameters, α and θ, corresponding to the stable component and Gamma component respectively. The moderate deviation principles are established for the… (More)
Using the high moment method and the Feynman-Kac semigroup technique, we obtain moderate deviations and laws of the iterated logarithm for the volume of the intersections of two and three dimensional Wiener sausages.
We establish a functional large deviation principle and a functional moderate deviation principle for Markov-modulated risk models with reinsurance by constructing an exponential martingale approach. Lundberg’s estimate of the ruin time is also presented.