Minimal integral representations of stable processes

• Autorzy: Rosiński, J.
• Języki publikacji: EN

Abstrakty

EN

Minimal integral representations are defined for general stochastic processes and completely characterized for stable processes (symmetric and asymmetric). In the stable case, minimal representations are described by rigid subsets of the Lp-spaces which are investigated here in detail. Exploiting this relationship, various tests for the minimality of representations of stable processes are obtained and used to verify this property for many representations of processes of interest.

Słowa kluczowe

EN

stable processes; stochastic integral representation; isometries on Lp-spaces

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2006
• Tom: Vol. 26, Fasc. 1
• Strony: 121--142
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Rosiński, J.

• Department of Mathematics, University of Tennessee Knoxville, TN 39996,

Bibliografia

• [1] S. Banach, Theorie des operations linéaires, 2nd ed., Chelsea, 1955.
• [2] C. D. Hardin Jr., Isometries on subspaces of 1У, Indiana Univ. Math. J. 30 (1981), pp. 449-465.
• [3] C. D. Hardin Jr., On the spectral representation of symmetric stable processes, J. Multivariate Anal. 12 (1982), pp. 385-401.
• [4] A. Janicki and A. Wer on, Simulation and Chaotic Behavior of α-stable Stochastic Processes, Marcel Dekker, 1994.
• [5] S. Kołodyński and J. Rosiński, Group self-similar stable processes in Rd, J. Theoret. Probab. 16 (2003), pp. 855-876.
• [6] J. Lamperti, On the isometries of certain function spaces, Pacific J. Math. 8 (1958), pp. 459-466.
• [7] V. Pipiras and M. S. Taqqu, The structure of self-similar stable mixed moving averages, Ann. Probab. 30 (2002), pp. 898-932.
• [8] V. Pipiras and M. S. Taqqu, Decomposition of self similar stable mixed moving averages, Probab. Theory Related Fields 123 (2002), pp. 412-452.
• [9] J. Rosiński, On the uniqueness of the spectral representation of stable processes, J. Theoret. Probab. 7 (1994), pp. 615-634.
• [10] J. Rosiński, Uniqueness of spectral representations of skewed stable processes and stationarity, in: Stochastic Analysis on Infinite Dimensional Spaces, H. Kunita and H.-H. Kuo (Eds.), Longman, 1994, pp. 264-273.
• [11] J. Rosiński, On the structure of stationary stable processes, Ann. Probab. 23 (1995), pp. 1163-1187.
• [12] J. Rosiński, Decomposition of stationary a-stable random fields, Ann. Probab. 28 (2001), pp. 1797-1813.
• [13] G. Samorodnitsky, Null flows, positive flows and the structure of stationary symmetric stable processes, Ann. Probab. 33 (2005), pp. 1782-1803.
• [14] G. Samorodnitsky and M. S. Taqqu, Non-Gaussian Stable Processes, Chapman and Hall, 1994.
• [15] R. Sikorski, Boolean Algebras, Academic Press, 1964.