A family of martingales generated by
Teoriâ slučajnyh processov, Tome 14 (2008) no. 2, pp. 139-144.

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An explicit procedure to construct a family of martingales generated by a process with independent increments is presented. The main tools are the polynomials that give the relationship between the moments and cumulants, and a set of martingales related to the jumps of the process called Teugels martingales.
Keywords: Process with independent increments
Mots-clés : Cumulants, Teugels martingales.
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Josep Lluís Solé; Frederic Utzet. A family of martingales generated by. Teoriâ slučajnyh processov, Tome 14 (2008) no. 2, pp. 139-144. http://geodesic.mathdoc.fr/item/THSP_2008_14_2_a13/

[1] M. Kendall, A. Stuart, The Advanced Theory of Statistics, v. 1, 4th edition, MacMillan, New York, 1977 | MR

[2] A. E. Kyprianou, Introductory Lectures on Fluctuations of Lévy Processes with Applications, Springer, Berlin, 2006 | MR

[3] P. McCullagh, Tensor Methods in Statistics, Chapman and Hall, London, 1987 | MR | Zbl

[4] P. A. Meyer, “Un cours sur les integrales stochastiques”, Séminaire de Probabilités X, Springer, New York, 1976, 245–400 (French) | MR

[5] D. Nualart, W. Schoutens, “Chaotic and predictable representation for Lévy processes”, Stochastic Process. Appl., 90 (2000), 109–122 | DOI | MR | Zbl

[6] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, 1999 | MR

[7] A. V. Skorohod, Random Processes with Independent Increments, Kluwer Academic Publ., Dordrecht, Boston, London, 1986 | MR

[8] J. L. Solé, F. Utzet, “Time-space harmonic polynomials relative to a Lévy process”, Bernoulli, 2007 | MR

[9] R. P. Stanley, Enumerative Combinatorics, v. 2, Cambridge University Press, Cambridge, 1999 | MR