A functional non-central limit theorem for multiple-stable processes with long-range dependence

A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals with heavy-tailed marginal distribution. Furthermore, the multiple stochastic integrals are built upon a large family of dynamical systems that are ergodic and conservative, leading to the long-range dependence phenomenon of the model. The limits constitute a new class of self-similar processes with stationary increments. They are represented by multiple stable integrals, where the integrands involve the local times of intersections of independent stationary stable regenerative sets.     

Central limit theorem for Banach space valued fuzzy random variables

In this paper we prove a central limit theorem for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.

     

A density theorem and its application

We compute the density of primes represented by a special quadratic form in a fixed square residue class. Using this result and a new method introduced by Thaine we prove the fact that for a prime p 3congruent to 3 modulo 4, the component e(p+1)/2of the p-Sylow subgroup of the ideal class group of Q(ζp) is trivial.     

一个因式相通定理及其应用

证明了一个因式相通定理,它是奇点理论中等价性定理的一个推广.这个定理表明单纯高阶项的开折对普适开折因式相通中的参数映射没有贡献.据此本文提出了一种因式相通中参数映射的简洁有效的近似计算方法     

A. S. Convergence of two-parameter banach space valued martingales and the radon-nikodym property of banach spaces

In this paper, we prove that under theF ₄ conditions, anyL log⁺ L bounded two-parameter Banach spece valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if theF ₄ condition is replaced by the weaker localF ₄ condition. Project supported by the National Natural Science Foundation of China and the State Education Commission Ph. D. Station Foundation     

A mean central limit theorem for weakly multiplicative systems and its application to lacunary trigonometric series

Summary In this paper, we discuss the rate of convergence in the mean central limit theorem for weakly multiplicative systems and apply this result to lacunary trigonometric series under probability measures on with Hölder continuous distribution function.     

A central limit theorem for measurements on the logarithmic scale and its application to dimension estimates

We show consistency and asymptotic normality of certain estimators for expected exponential growth rates under i.i.d. observations. These statistical functionals are of the form

T(F)=∫log∫h(x,y)F(dx)F(dy)     

Bmo boundedness for banach space valued singular integrals

In this paper, we consider a class of Banach space valued singular integrals. The Lp boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundednessfor the classic g-function and the Marcinkiewicz integral. Some known results are improved.     

A theorem on parastatistics and its application

Proceeding from the assumption that nature chooses a riskless strategy, we consequently obtain a distribution over parastatistics. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 3, pp. 511–512, March, 2007.     

Uniform bounds in the central limit theorem for C(S) valued martingales

Vilnius University. Published in Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 1, pp. 146–165, January–March, 1991.