A central limit theorem for independent summands with infinite variances

A central limit theorem for independent summands having variances tending to infinity at a certain rate is obtained. This result is extended to the cases where the sample size is random and where the random variables are vector-valued.     

Multidimensional local central limit theorem of some non-uniformly hyperbolic systems

We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously independent, then f satisfies the multidimensional central limit theorem. Moreover if f is aperiodic, then f satisfies the local multidimensional central limit theorem.     

A central limit theorem for trigonometric series with bounded gaps

In this paper it is proved that there exists a sequence {n _k } of integers with 1 ?? n _k+1 ? n _k ?? 5 such that the distribution of ${(\cos 2\pi n_1 x + \dots + \cos 2\pi n_{N}) / \sqrt N}$ on ([?0, 1?], B, dx) converges to a Gaussian distribution. It gives an affirmative answer to the long standing problem on lacunary trigonometric series which ask the existence of series with bounded gaps satisfying a central limit theorem.     

On limit classes of bounded perturbations

We obtain sufficient conditions for a given class of piecewise continuous bounded perturbations to be a limit class, i.e., to admit the computation of the least upper bound for the exponents of linear differential systems with perturbations in that class by a formula similar to well-known formulas for the central and exponential exponents.     

Uniformly bounded limit of fractional homomorphisms

We show that a bounded homomorphism is equivalent to a uniformly bounded family of fractional homomorphisms for any 0$">. We add this characterization to the Widder-Arendt-Kisynski theorem and relate it to -times integrated semigroups.

     

Multidimensional high-field limit of the electrostatic Vlasov-Poisson-Fokker-Planck system

In this paper, the high-field limit of the Vlasov-Poisson-Fokker-Planck system for charged particles is rigorously derived. The first result is obtained in any space dimension by using modulated energy techniques. It requires the smoothness of the solutions of the limit problem. In dimension 2, it is possible to handle more general data by using methods developed for a diagonal defect measures theory. The convergence of the concentration of particles is obtained in the space of bounded measures. In both cases, the limit of the sequence of densities of distribution functions is shown to solve a nonlinear system of partial differential equations which is related to Ohm's law.     

Regularity criterion for generalized Newtonian fluids in bounded domains

The regularity of a non-Newtonian flow in a domain with a boundary cannot be treated easily because of the nonlinear viscosity term and the global property of the pressure. A distance function was used in a previous study to obtain a strong solution. In the present study, using the distance function idea, we obtain Serrin-type regularity criteria for the vorticity and the velocity with regard to non-Newtonian equations with shear-dependent viscosity in a bounded domain.     

Multidimensional limit theorems in models with categorized-time absolute priorities

One describes the class of all possible limit distributions for the random vector of waiting times in a queueing system with absolute priorities.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 131–155, 1986.     

Blow-up criterion for 2-D Boussinesq equations in bounded domain

We extend the results for 2-D Boussinesq equations from ℝ² to a bounded domain Ω. First, as for the existence of weak solutions, we transform Boussinesq equations to a nonlinear evolution equation U _t + A(t, U) = 0. In stead of using the methods of fundamental solutions in the case of entire ℝ², we study the qualities of F(u, υ) = (u · ▽)υ to get some useful estimates for A(t, U), which helps us to conclude the local-in-time existence and uniqueness of solutions. Second, as for blow-up criterions, we use energy methods, Sobolev inequalities and Gronwall inequality to control and by and . Furthermore, can control by using vorticity transportation equations. At last, can control . Thus, we can find a blow-up criterion in the form of .      

Uniqueness of limit cycles bounded by two invariant parabolas

In this paper we consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas.     

Multidimensional travelling waves in the monostable case

We prove existence and stability of multidimensional travelling waves for monotone parabolic systems of equations. We consider the so-called monostable case for which one of the limiting values at infinity is stable with respect to the limiting problem and another one is unstable.     

On the central limit theorem in Banach spaces

It is shown, with the use of a concentration inequality of LeCam, that associated with an infinitely divisible random variable with values in a separable Banach space there is a Lévy-Khintchine formula. A partial converse of this fact is also proved. Relations between the continuity of the compound Poisson and the Gaussian variables associated with a Lévy measure are studied. A central limit theorem is obtained and examples are given.