Zapała, August Michał Reflection principle and strong Markov property for multiparameter group- valued additive processes. (English) Zbl 0705.60062 Stochastic Processes Appl. 36, No. 1, 15-32 (1990). The author considers group-valued additive processes with randomly changing multidimensional time parameters. He proves a general reflection principle and the strong Markov property for multiparameter additive processes taking values in a \(T_ 0\) topological Abelian group. The case of noncommutative groups is also discussed. Reviewer: Z.Rychlik Cited in 1 Document MSC: 60J99 Markov processes 60G60 Random fields 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization 60G40 Stopping times; optimal stopping problems; gambling theory Keywords:group-valued additive processes; reflection principle; strong Markov property; multiparameter additive processes PDFBibTeX XMLCite \textit{A. M. Zapała}, Stochastic Processes Appl. 36, No. 1, 15--32 (1990; Zbl 0705.60062) Full Text: DOI References: [1] Adler, R. J.; Monrad, D.; Scissors, R. H.; Wilson, R., Representations, decompositions and sample function continuity of random fields with independent increments, Stochastic Process. Appl., 15, 3-30 (1983) · Zbl 0507.60043 [2] Billingsley, P., Convergence of Probability Measures (1968), Wiley: Wiley New York · Zbl 0172.21201 [3] Hewitt, E.; Ross, K. A., Abstract Harmonic Analysis (1963), Springer: Springer Berlin · Zbl 0115.10603 [4] Ivanoff, B. G., The function space \(D(〈0, ∞)^q)\), Canad. J. Statist., 8, 179-191 (1980) · Zbl 0467.60009 [5] Skorohod, A. V., Stochastic Processes with Independent Increments (1986), Nauka: Nauka Moscow, (in Russian) [6] Vahania, N. N.; Tarieladze, V. I.; Chobanian, S. A., Probability Distributions in Banach Spaces (1985), Nauka: Nauka Moscow, (in Russian) [7] Walsh, J. B., Martingales with a multidimensional parameter and stochastic integrals in the plane, (Lecture Notes in Math., Vol. 1215 (1986), Springer: Springer Berlin), 329-491 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.