On the conditional intensity of a random measure

Pierre Jacob; Paulo Eduardo Oliveira

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 1, page 103-109
  • ISSN: 0010-2628

Abstract

top
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.

How to cite

top

Jacob, Pierre, and Oliveira, Paulo Eduardo. "On the conditional intensity of a random measure." Commentationes Mathematicae Universitatis Carolinae 35.1 (1994): 103-109. <http://eudml.org/doc/247591>.

@article{Jacob1994,
abstract = {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.},
author = {Jacob, Pierre, Oliveira, Paulo Eduardo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {random measure; point process; conditional intensity; absolute continuity; martingales; martingales; conditional intensity; random measure},
language = {eng},
number = {1},
pages = {103-109},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the conditional intensity of a random measure},
url = {http://eudml.org/doc/247591},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Jacob, Pierre
AU - Oliveira, Paulo Eduardo
TI - On the conditional intensity of a random measure
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 1
SP - 103
EP - 109
AB - 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.
LA - eng
KW - random measure; point process; conditional intensity; absolute continuity; martingales; martingales; conditional intensity; random measure
UR - http://eudml.org/doc/247591
ER -

References

top
  1. Billingsley P., Probability and Measure, Wiley, 1979. Zbl0822.60002MR0534323
  2. Kallenberg O., On conditional intensities of point processes, Z. Wahrsch. Verw. Geb. 41 (1978), 205-220. (1978) Zbl0349.60056MR0461654
  3. Kallenberg O., L p intensities of random measures, stochastic processes and their applications, Stoch. Proc. and Appl. 9 (1979), 155-161. (1979) MR0548835
  4. Kallenberg O., Random Measures, Academic Press, 1983. Zbl0694.60030MR0818219
  5. Kopp P.E, Martingales and Stochastic Integrals, Cambridge University Press, 1984. Zbl1152.60043MR0774050
  6. Papangelou F., The conditional intensity of general point processes and an application to line processes, Z. Wahrsch. Verw. Geb. 28 (1974), 207-226. (1974) Zbl0265.60047MR0373000
  7. Papangelou F., Point processes on spaces of flats and other homogeneous spaces, Math. Proc. Cambridge Phil. Soc. 80 (1976), 297-314. (1976) Zbl0342.60042MR0410845
  8. Varsei A., Ph.D. thesis, 1978. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.