Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis

In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas for the convolutions of Bernoulli and Euler polynomials, expressed via Apostol-Bernoulli polynomials of higher order.Comment: 8 pages, submitte

Laws of the single logarithm for delayed sums of random fields

We extend a law of the single logarithm for delayed sums by Lai to delayed sums of random fields. A law for subsequences, which also includes the one-dimensional case, is obtained in passing.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ103 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Discretized normal approximation by Stein's method

We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of i.i.d. Bernoulli random variables, the number of vertices with a given degree in the Erd\"{o}s-R\'{e}nyi random graph, and the uniform multinomial occupancy model.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ527 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Asymptotic behavior of CLS estimators for 22-type doubly symmetric critical Galton-Watson processes with immigration

In this paper, the asymptotic behavior of the conditional least squares (CLS) estimators of the offspring means $(\alpha,\beta)$ and of the criticality parameter $\varrho:=\alpha+\beta$ for a $2$-type critical doubly symmetric positively regular Galton-Watson branching process with immigration is described.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ556 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

"Bernoulli" Levitation

"Bernoulli" levitation is the basis of many popular counter-intuitive physics demonstrations. However, few of these lend themselves to a quantitative description without recourse to computational fluid dynamics. Levitation of a flat plate is the exception, and we present here a straightforward analysis which illustrates several principles of fluid mechanics in a pedagogically useful way.Comment: 12 pages, 8 figures. Submitted to Am. J. Phy

The AEP algorithm for the fast computation of the distribution of the sum of dependent random variables

We propose a new algorithm to compute numerically the distribution function of the sum of $d$ dependent, non-negative random variables with given joint distribution.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ284 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Sojourn measures of Student and Fisher-Snedecor random fields

Limit theorems for the volumes of excursion sets of weakly and strongly dependent heavy-tailed random fields are proved. Some generalizations to sojourn measures above moving levels and for cross-correlated scenarios are presented. Special attention is paid to Student and Fisher-Snedecor random fields. Some simulation results are also presented.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ529 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm