| Title:
|
On the conditional intensity of a random measure (English) |
| Author:
|
Jacob, Pierre |
| Author:
|
Oliveira, Paulo Eduardo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
103-109 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
random measure |
| Keyword:
|
point process |
| Keyword:
|
conditional intensity |
| Keyword:
|
absolute continuity |
| Keyword:
|
martingales |
| MSC:
|
60G44 |
| MSC:
|
60G55 |
| MSC:
|
60G57 |
| idZBL:
|
Zbl 0795.60034 |
| idMR:
|
MR1292587 |
| . |
| Date available:
|
2009-01-08T18:09:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118645 |
| . |
| Reference:
|
[1] Billingsley P.: Probability and Measure.Wiley, 1979. Zbl 0822.60002, MR 0534323 |
| Reference:
|
[2] Kallenberg O.: On conditional intensities of point processes.Z. Wahrsch. Verw. Geb. 41 (1978), 205-220. Zbl 0349.60056, MR 0461654 |
| Reference:
|
[3] Kallenberg O.: L$_p$ intensities of random measures, stochastic processes and their applications.Stoch. Proc. and Appl. 9 (1979), 155-161. MR 0548835 |
| Reference:
|
[4] Kallenberg O.: Random Measures.Academic Press, 1983. Zbl 0694.60030, MR 0818219 |
| Reference:
|
[5] Kopp P.E: Martingales and Stochastic Integrals.Cambridge University Press, 1984. Zbl 1152.60043, MR 0774050 |
| Reference:
|
[6] Papangelou F.: The conditional intensity of general point processes and an application to line processes.Z. Wahrsch. Verw. Geb. 28 (1974), 207-226. Zbl 0265.60047, MR 0373000 |
| Reference:
|
[7] Papangelou F.: Point processes on spaces of flats and other homogeneous spaces.Math. Proc. Cambridge Phil. Soc. 80 (1976), 297-314. Zbl 0342.60042, MR 0410845 |
| Reference:
|
[8] Varsei A.: Ph.D. thesis.1978. |
| . |
