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Using the method of transportation-information inequality introduced in , we establish Bernstein type's concentration inequalities for empirical means 1 t t 0 g(X s)ds where g is a unbounded observable of the symmetric Markov process (X t). Three approaches are proposed : functional inequalities approach ; Lyapunov function method ; and an approach… (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)
Some deviation inequalities and moderate deviation principles for the maximum likelihood esti-mators of parameters in an Ornstein-Uhlenbeck process with linear drift are established by the logarithmic Sobolev inequality and the exponential martingale method.
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.
The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing non-negative 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)