We classify the reverse process {Xn} of a multitype Galton-Watson process {Zn}. In the positive recurrent cases we give the stationary measure for {Xn} explicitly, and in the critical case, supposing that all the second moments of Z1 are finite, we establish the convergence in law to a gamma...

Let X and Y be random vectors of the same dimension such that Y has a normal distribution with mean vector O and covariance matrix R. Let g(x), x=0, be a bounded nonincreasing function. X is said to be g-subordinate to Y if Eeiu'X = g(u'Ru) for all real vectors u of the same dimension as X. This...

Let Yn, n=1, be a sequence of integrable random variables with EYn = xn1[beta]1 + xn2[beta]2 + ... + xnp[beta]p, where the xij's are known and [beta]T = ([beta]1, [beta]2,..., [beta]p) unknown. Let bn be the least-squares estimator of [beta] based on Y1, Y2,..., Yn. Weak consistency of bn, n=1,...

The Fréchet distance between two multivariate normal distributions having means [mu]X, [mu]Y and covariance matrices [Sigma]X, [Sigma]Y is shown to be given by d2 = [mu]X - [mu]Y2 + tr([Sigma]X + [Sigma]Y - 2([Sigma]X[Sigma]Y)1/2). The quantity d0 given by d02 = tr([Sigma]X + [Sigma]Y -...

Several new characterizations of nuclearity in Fréchet spaces are proved. The most important one states tat a Fréchet space is nuclear if and only if every mean bounded amart is strongly a.s. convergent. This extends the result in [[2], 1798-1799] in a more positive way, and gives a different...

Limit theorems for the multitype branching random walk as n -- [infinity] are given (n is the generation number) in the case in which the branching process has a mean matrix which is not positive regular. In particular, the existence of steady state distributions is proven in the subcritical...

The so-called spectral representation theorem for stable processes linearly imbeds each symmetric stable process of index p into Lp (0 p = 2). We use the theory of Lp isometries for 0 p 2 to study the uniqueness of this representation for the non-Gaussian stable processes. We also determine...

Let 4 and 4 be the spaces of generalized Brownian functionals of the white noises B and b, respectively. A Fourier transform from 4 into 4 is defined by [phi](b) = [integral operator]0*: exp[-i [integral operator]1b(t) B(t) dt]: 1), where : : denotes the renormalization with respect to b and...

We shall define the concept of fourth-order strong mixing rates and study their properties. Results are useful for establishing a condition of the form (*) [Sigma]a,b,c cum(Xo, Xa, Xb, Xc) [infinity] or [integral operator]cum(Xo, Xa, Xb, Xc) da db dc [infinity] for dependent random variables...

The r-quick limit points of normalized sample paths and empirical distribution functions of mixing processes are characterized. An r-quick version of Bahadur-Kiefer-type representation for sample quantiles is established, which yields the r-quick limit points of quantile processes. These results...