Integrability of expected increments of point processes and a related random change of scale. (English) Zbl 0236.60036


60G99 Stochastic processes
Full Text: DOI


[1] N. Bourbaki, Eléments de mathématique. XIII. Première partie: Les structures fondamentales de l’analyse. Livre VI: Intégration. Chapitre I: Inégalités de convexité. Chapitre II: Espaces de Riesz. Chapitre III: Mesures sur les espaces localement compacts. Chapitre IV: Prolongement d’une mesure; espaces \?^{\?}, Actualités Sci. Ind., no. 1175, Hermann et Cie, Paris, 1952 (French). · Zbl 0049.31703
[2] Werner Fieger, Die Anzahl der \?-Niveau-Kreuzungspunkte von stochastischen Prozessen, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 18 (1971), 227 – 260 (German). · Zbl 0199.52403 · doi:10.1007/BF00563139
[3] Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. · Zbl 0138.10401
[4] K. Murali Rao, On decomposition theorems of Meyer, Math. Scand. 24 (1969), 66 – 78. · Zbl 0193.45501 · doi:10.7146/math.scand.a-10920
[5] F. Papangelou, On the Palm probabilities of processes of points and processes of lines, Stochastic geometry (a tribute to the memory of Rollo Davidson), Wiley, London, 1974, pp. 114 – 147. · Zbl 0293.60046
[6] -, Summary of some results on point and line processes, Proc. IBM Conference on Stochastic Point Processes (held August 1971).
[7] Frédéric Riesz and Béla Sz.-Nagy, Leçons d’analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1953 (French). 2ème éd. · Zbl 0051.08403
[8] Czesław Ryll-Nardzewski, Remarks on processes of calls, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, Univ. California Press, Berkeley, Calif., 1961, pp. 455 – 465.
[9] František Zítek, The theory of ordinary streams, Select. Transl. Math. Statist. and Probability, Vol. 2, American Mathematical Society, Providence, R.I., 1962, pp. 241 – 251.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.