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We prove a local limit the sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bo...
We develop a Hungarian construction for the partial sum process of independent non-identically distributed random variables. The process is indexed by functions f from a class H, but the supremum over...
Abstract: For a given pair of positive integers $d$ and $N$ with $N \geq 2$, for strictly stationary random fields that are indexed by the $d$-dimensional integer lattice and satisfy $N$-tuplewise ind...
In this paper we discus on the Borel-Cantelli lemma when the condition of independent events is replaced by negative quadrant dependent condition.
We consider products of independent random matrices with independent entries.The limit distribution of the expected empirical distribution of eigenvalues of such products is computed. Let X()jk , 1 ≤...
Consider a system of particles evolving as independent and iden-tically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity ~v, the c...
This note gives the convergence rate in the central limit theorem and the random central limit theorem of some functions of the average of independent random variables.
On the limit behaviour of random sums of independent random variables。
Weak convergence of random sums of infima of independent random variables。
We give tbe rate of convergence in the central limit theorem and the random central limit theorem for functions belonging to the class I of all real differentiable functions g such that gr E L(1).
The Levy and the Dudley metrics are used to give estimates of the rate convergence in the centrat- limit theorem for some functions of the average of independent random variables.
Topology of the convergence in probability on a linear span of a sequence of independent random variables。
Weak convergence to the Brownian motion of the partial sums of infima of independent random variables。
On the rate of convergence to Brownian motion of the partial sums of infima of independent random variables。

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