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Convolution equivalence and distributions of random sums
A serious gap in the Proof of Pakes’s paper on the convolution equivalence of infinitely divisible distributions on the line is completely closed. It...
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Loop-Erased Random Walk on Finite Graphs and the Rayleigh Process
Let ( G n )
n =1 ∞ be a sequence of finite graphs, and let Y t be the length of a loop-erased random walk on G n after t steps. We show that for a... -
Gradient Estimate of the Heat Kernel on Modified Graphs
We obtain a condition on the modification of graphs which guarantees the preservation of the Gaussian upper bound for the gradient of the heat kernel.
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Asymptotic expansions for infinite weighted convolutions of rapidly varying subexponential distributions
We establish some asymptotic expansions for infinite weighted convolutions of distributions having rapidly varying subexponential tails. Examples are...
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On the Local Times of Transient Random Walks
We study the properties of the local and occupation times of certain transient random walks. First, our recent results concerning simple symmetric...
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On the harmonic averages of numerical sequences
In recent years, the almost sure central limit theorem attracted widespread attention in Probability Theory. It involves the harmonic (also called...
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Strengthening classical results on convergence rates in strong limit theorems
Let X 1 , X 2 , . . . be i.i.d. random variables, and set S n = X 1 + . . . + X n . Several authors proved convergence of series of the type f ( ɛ )=∑ ...
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Tail probability approximations for Student's t-statistics
In this paper, we derive saddlepoint approximations for Student's t -statistics for strongly nonlattice random variables without moment conditions....
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Divisors, spin sums and the functional equation of the Zeta-Riemann function
Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><
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An optimal bound on the tail distribution of the number of recurrences of an event in product spaces
Let X 1 , X 2 ,... be independent random variables and a a positive real number. For the sake of illustration, suppose A is the event that | X ...
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Dimensionality Reduction in Extremal Problems for Moments of Linear Combinations of Vectors with Random Coefficients
It is shown that $$\sup \left\{ {E\varphi \left( {{{{\left\|...
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Fast graphs for the random walker
Consider the time T oz when the random walk on a weighted graph started at the vertex o first hits the vertex set z . We present lower bounds for T ...