Convergence of the Intensity Measure of Random Measure Associated to the Random Generalized Cookie-Cutter Set
Fangfang Liao, Zu-Guo Yu · 2007
A random generalized cookie-cutter set K(superscript T) on [0,T] is constructed. Let K(superscript n) be the n-th level set of K(superscript T) in the process of construction. Then a memory function on K(superscript n) is defined. Based on this memory function, a random probability measure ф(superscript n) (τ) on K(superscript n) is defined. Let Ψ(superscript n)(•)=Eф(superscript n)(•), where Ψ(superscript n), is the intensity measure of the random measure ф(superscript n). At last it is proved that the sequence {Ψ(superscript n)} is weakly convergent and Ψ=limΨ(superscript n)