×

Multivariate point processes: Predictable projection, Radon-Nikodym derivatives representation of martingales. (English) Zbl 0302.60032


MSC:

60G99 Stochastic processes
60G35 Signal detection and filtering (aspects of stochastic processes)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Benveniste, A.; Jacod, J., Systèmes de Lévy des processus de Markov, Invent. Math., 21, 183-198 (1973) · Zbl 0265.60074
[2] Boel, R.; Varaiya, P.; Wong, E., Martingales on jump processes I, II (1973), Berkeley: El. Res. Lab., Berkeley
[3] Brémaud, P., A martingale approach to point processes, PhD thesis (1972), Berkeley: El. Res. Lab., Berkeley
[4] Brémaud, P., The martingale theory of point processes over the real half-line, IRIA Int. Colloquium on Control Theory (1974), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York · Zbl 0372.60068
[5] Chou, C. S.; Meyer, P. A., La représentation des martingales relatives à un processus ponctuel discret, C. R. Acad. Sci. Paris, A, 278, 1561-1563 (1974) · Zbl 0316.60035
[6] Dellacherie, C., Un exemple de la théorie génerale des processus, Sém. Proba. IV, Lecture Notes 124 (1970), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York
[7] Dellacherie, C., Capacités et processus stochastiques (1972), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York · Zbl 0246.60032
[8] Grigelionis, B., On nonlinear filtering theory and absolute continuity of measures, corresponding to stochastic processes (1973), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York · Zbl 0262.60026
[9] Ito, K.; Watanabe, S., Transformation of Markov processes by multiplicative functionals, Ann. Inst. Fourier, XV, 13-30 (1965) · Zbl 0141.15103
[10] Jacod, J.: On the stochastic intensity of a random point process over the half-line. Tech. Report 51, Dept. Stat. Princeton University (1973)
[11] Kailath, T., The structure of Radon-Nikodym derivatives with respect to Wiener and related measures, Ann. Math. Statist., 42, 1054-1067 (1971) · Zbl 0246.60041
[12] Meyer, P. A., Probability and potential (1966), Waltham: Blaisdell, Waltham
[13] Meyer, P. A., Processus ponctuels selon K. Ito, Sém. Proba. V (1971), Berlin, Heidelberg, New York: Springer, Berlin, Heidelberg, New York
[14] Meyer, P. A., Processus ponctuels selon K. Ito, Sém. Proba. V (1971), Berlin: Springer, Berlin
[15] Orey, S.: Radon-Nikodym derivative of probability measures: martingale methods. Dpt. Found. Math. Sc., Tokyo Un. of Education (1974)
[16] Papangelou, F., Integrability of expected increments of point processes and a related change of scale, Trans. Amer. Math. Soc., 165, 483-506 (1972) · Zbl 0236.60036
[17] Rubin, I., Regular point processes and their detection, IEEE, Trans. Information Theory, 18, 5 (1972)
[18] Segall, A., Kailath, T.: Radon-Nikodym derivatives with respect to measures induced by discontinuous independent-increments processes. To appear · Zbl 0312.60023
[19] Segall, A., Kailath, T.: On the representation of martingales as stochastic integrals. To appear · Zbl 0298.60050
[20] Skorohod, A. V.: Random processes with independent increments, Rep. AD 645769, Foreign Technology Division
[21] Snyder, D., Filtering and detection for doubly stochastic Poisson processes, IEEE, Trans. Information Theory, 18, 1 (1972)
[22] van Schuppen, J. H., Wong, E.: Transformations of local martingales under a change of law. El. Res. Lab. Berkeley, M-385 (1973) · Zbl 0321.60040
[23] Watanabe, S., On discontinuous additive functionals and Lévy measures of a Markov process, Japan. J. Math., 34, 53-79 (1964) · Zbl 0141.15703
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.