LIMIT THEOREMS FOR MULTITYPE CONTINUOUS TIME MARKOV BRANCHING PROCESSES .2. CASE OF AN ARBITRARY LINEAR FUNCTIONAL

In this sequel to [1] we develop limit theorems for the stochastic process {η · X(t); t>=0} where η is a general vector in the k dimensional complex vector space. Using the spectral representation of M(t) one can define for η three parameters: a real number a=a(η), an integer γ=γ(η) and an index set I=I(η). If 2 a<λ1 then there exist random variables Yjand real numbers bjfor jεI (η) such that {Mathematical expression} converges to zero in mean square. If 2 a<=λ1 the same results as in the eigenvector case hold. © 1969 Springer-Verlag.