We give a counterexample to the Strong Bang-Bang Conjecture according to which any 3 - 3 embeddable matrix can be expressed as a product of six Poisson matrices. We exhibit a 3 - 3 embeddable matrix which can be expressed as a product of seven but not six Poisson matrices. We show that an...

An approximation theorem of stochastic differential equations driven by semimartingales is proved, based on approximation of semimartingales by a sequence of processes with piecewise monotonic sample functions.

It is shown that every genuinely d-dimensional operator-self-decomposable distribution is absolutely continuous.

Optional increasing paths passing through a given stopping point are studied. A characterization of the two extreme optional increasing paths is obtained. The past of a stopping point is defined, and a description of the largest stopping point smaller than two given stopping points is given. A...

A necessary and sufficient condition is given for the existence of stationary probability distributions of a non-Markovian model with linear transition rule. Similar to the Markovian case, stationary probability distributions are characterized as eigenvectors of nonnegative matrices. The model...

A recent paper by Mack and Rosenblatt (J. Multivar. Anal. 9 (1979), 1-15) has shown that near neighbour estimators of a density may perform more poorly than other kernel-type estimators, particularly for x values in the tail of a distribution. In order to overcome the difficulties discovered by...

As is well known, in full rank multivariate exponential families, tests of Neyman structure are uniformly most powerful unbiased for one-sided problems. For the case of lattice distributions, the power of these tests--evaluated at contiguous alternatives--is approximated by asymptotic expansions...

It is shown that for the elements X of a large class of subgaussian random variables with values in (C(S), ·[infinity]) the existence of a probability measure [lambda] on S such that: (where [psi] denotes the inverse function of x -- exp x2L2x) is sufficient to imply that X satisfies the law...

Let x(t), t = 1,..., T, be generated by a zero mean stationary process and let I([omega]) = [Sigma]x(t)expit[omega]2/T be the periodogram. Under general conditions, and in particular assuming only a finite 2nd moment, it is shown that max[omega]I([omega])/{2[pi]f([omega])logT} = 1, a.s., and...

The unified theory of Bayes estimation in linear models is presented, using a coordinate-free approach. The results are applied to the problem of linear and quadratic estimation in linear regression model.