Time sensitive functionals of marked Cox processes

This paper continues studies on amultivariate marked Cox process Ct observed upon some random epochs τ = {τ1, τ2, . . .} initiated in [J. Math. Anal. Appl. 293 (2004) 1–13]. The goal is to connect the continuous time parameter process Ct with Cτ for which closed-form transforms were presented in that paper. This work does not only restore some or much of the information on Ct lost due to its limited observation, but it also manages to scrutinize the behavior of Cτ around the first passage time of Cτ (that takes place upon one of the observation epochs τ ) within some random time intervals. Again, analytically tractable formulas for functionals of Cτ are derived.  2004 Elsevier Inc. All rights reserved