论文信息 - Derived random measures

Derived random measures

A derived random measure is constructed by integration of a random process with respect to a random measure independent of that process. Basic distributional properties, a continuity theorem, sample path properties, a strong law of large numbers, and a central limit theorem for derived random measures are established. Applications are given to compounding and thinning of point processes and the measure of a random set.

Alan F. Karr | A. Karr

[1] J. Neveu,et al. Mathematical foundations of the calculus of probability , 1965 .

[2] Olav Kallenberg,et al. Limits of compound and thinned point processes , 1975, Journal of Applied Probability.

[3] Richard F. Serfozo,et al. Processes with conditional stationary independent increments , 1972, Journal of Applied Probability.

[4] O. Kallenberg. Characterization and convergence of random measures and point processes , 1973 .

[5] P. Billingsley,et al. Convergence of Probability Measures , 1969 .

[6] J. Kingman,et al. Completely random measures. , 1967 .

[7] Johannes Kerstan,et al. Unbegrenzt teilbare Punktprozesse , 1974 .

[8] O. Kallenberg. On the Existence and Path Properties of Stochastic Integrals , 1975 .

[9] R. Smythe. Ergodic properties of marked point processes in $R^r$ , 1975 .