Coquet, F.; Mémin, J.; Mackevičius, V. Some examples and counterexamples of convergence of \(\sigma\)-algebras and filtrations. (English) Zbl 0990.60035 Lith. Math. J. 40, No. 3, 228-235 (2000) and Liet. Mat. Rink. 40, No. 3, 295-306 (2000). Weak convergence problems of \(\sigma\)-algebras and of filtrations are discussed. The authors show that some well-known properties related to convergence of \(\sigma\)-algebras are not extendable to convergence of filtrations. They study in more detail the case of one-jump point processes and the corresponding generated filtrations. Reviewer: Elisaveta Pancheva (Sofia) Cited in 4 Documents MSC: 60G07 General theory of stochastic processes 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) Keywords:convergence of \(\sigma\)-algebras; filtrations; Skorokhod topology; point processes PDFBibTeX XMLCite \textit{F. Coquet} et al., Lith. Math. J. 40, No. 3, 228--235 (2000) and Liet. Mat. Rink. 40, No. 3, 295--306 (2000; Zbl 0990.60035) Full Text: DOI References: [1] P. Billingsley,Probability and Measure, Wiley (1979). [2] F. Coquet, V. Mackevičius, and J. Mémin, Stability inD of martingales and backward equations under discretization of filtration,Stochastic Process. Appl. 75, 235–248 (1998). · Zbl 0932.60047 [3] F. Coquet, J. Mémin, and L. Słominski, On weak convergence of filtrations,Lecture Notes in Math., Séminaire de Probabilités XXXV, to appear (2000). · Zbl 0987.60009 [4] C. Dellacherie, Un exemple de la théorie générale des processus,Lecture Notes in Math.,214,Séminaire de Probabilités IV, 60–70 (1970). [5] C. Dellacherie and P. A. Meyer,Probabilités et Potentiel, vol. 2: Théorie des Martingales, Hermann (1980). [6] D. N. Hoover, Convergence in distribution and Skorokhod convergence for the general theory of processes,Probab. Th. Rel. Fields,89, 239–259 (1991). · Zbl 0725.60005 [7] J. Jacod and A. N. Shiryaev,Limit Theorems for Stochastic Processes, Springer, Berlin (1987). · Zbl 0635.60021 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.