Qualitative and asymptotic properties of stochastic integrals related to random marked point processes

Abstract

For real-valued random fields {v(t); t∈R ^d } of the form where is a random marked point process in R^dqualitative and asymptotic properties are investigated such as moment formulas, inequalities, in particular bounds by comparing {x _n} to a Poisson point process, as well as continuity and asymptotic normality of characteristics of {v(t)} if the underlying marked point process or the response functions f _t vary in a suitable manner.

Keywords:

• Short noise
• higher moments
• cumulates
• Poisson bounds
• continuity
• asymptotic normality

AMS 1980 Subject Classification:

• Primary:60 G 55