2 citations · 3 across the 5 of their papers we have counts for
6 papers
Polynomial Time Computable Triangular Arrays For Almost Sure Convergence
Vladimir Dobric, Marina Skyers, Lee J. Stanley
For 0 < x < 1, take the binary expansion with infinitely many 0's, replace each 0 with -1, this gives the polarized binary expansion of x. Let R_i(x) be the ith "polarized bit" and…
Polynomial Time Relatively Computable Triangular Arrays in a Multinomial Setting
Vladimir Dobric, Patricia Garmirian, Lee J. Stanley
We extend the methods and results of [arXiv 1603.04896] to the setting of multinomial distributions satisfying certain properties. These include all the multinomial distributions a…
A New Direct Proof of the Central Limit Theorem
Vladimir Dobric, Patricia Garmirian
We prove the Central Limit Theorem (CLT) from the definition of weak convergence using the Haar wavelet basis, calculus, and elementary probability. The use of the Haar basis pinpo…
Lower bounds for distribution of suprema of Brownian increments and Brownian motion normalized by the corresponding modulus functions
Vladimir Dobric, Lisa Marano
The Lévy-Ciesielski Construction of Brownian motion is used to determine non-asymptotic estimates for the maximal deviation of increments of a Brownian motion process $(W_{t})_{t\i…
Stability properties for a compactly supported prescale function
V. Dobric, R. F. Gundy, P. Hitczenko
We show that if is a continuous, minimally supported prescale function, then its translates are linearly independent on any set of positive measure in the unit interval. This g…
Characterizations of orthonormal scale functions: a probabilistic approach
V. Dobric, R. F. Gundy, P. Hitczenko
The construction of a multiresolution analysis starts with specification of a scale function. The Fourier transform of this function is defined by an infinite product. The converge…