Article
Keywords:
random measure; point process; conditional intensity; absolute continuity; martingales
Summary:
We prove the existence of the conditional intensity of a random measure that is absolutely continuous with respect to its mean; when there exists an L$^{p}$-intensity, $p>1$, the conditional intensity is obtained at the same time almost surely and in the mean.
References:
[2] Kallenberg O.:
On conditional intensities of point processes. Z. Wahrsch. Verw. Geb. 41 (1978), 205-220.
MR 0461654 |
Zbl 0349.60056
[3] Kallenberg O.:
L$_p$ intensities of random measures, stochastic processes and their applications. Stoch. Proc. and Appl. 9 (1979), 155-161.
MR 0548835
[6] Papangelou F.:
The conditional intensity of general point processes and an application to line processes. Z. Wahrsch. Verw. Geb. 28 (1974), 207-226.
MR 0373000 |
Zbl 0265.60047
[7] Papangelou F.:
Point processes on spaces of flats and other homogeneous spaces. Math. Proc. Cambridge Phil. Soc. 80 (1976), 297-314.
MR 0410845 |
Zbl 0342.60042
[8] Varsei A.: Ph.D. thesis. 1978.