We consider harmonic moments of branching processes in general random environments.For a sequence of square integrable random variables,we give some conditions such that there is apositive constant c that every variable in this sequence belong to Ac or A'c uniformly.
This article is a continuation of[9].Based on the discussion of random Kolmogorov forward(backward)equations,for any given q-matrix in random environment, Q(θ)=(q(θ;x,y),x,y∈X),an infinite class of q-processes in random environments satisfying the random Kolmogorov forward(backward)equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward(backward)equation are constructed.
This article presents a statistic for testing the sphericity in a GMANOVA- MANOVA model with normal error. It is shown that the null distribution of this statistic is beta and its nonnull distribution is given in series form of beta distributions.
The concepts of Markov process in random environment,q-matrix in random environment,and q-process in random environment are introduced.The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.
