Stochastic complex integrals associated with homogeneous independently scattered random measures on the line

• Autorzy: Yamamuro, Kouji
• Języki publikacji: EN

Abstrakty

EN

Complex integrals associated with homogeneous independently scattered random measures on the line are discussed. Theorems corresponding to Cauchy’s theorem and the residue theorem are given. Furthermore, the converse of Cauchy’s theorem is discussed.

Słowa kluczowe

EN

stochastic integral; infinitely divisible distribution; Lévy process; complex integral

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 1
• Strony: 219--236
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Yamamuro, Kouji

• Faculty of Engineering, Gifu University, Gifu 501-1193, Japan,

Bibliografia

• [1] T. Aoyama and M. Maejima, Charcterizations of subclasses of type G distributions on Rd by stochastic integral representations, Bernoulli 13 (2007), pp. 148-160.
• [2] O. E. Barndorff-Nielsen, M. Maejima, and K. Sato, Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations, Bernoulli 12 (1) (2006), pp. 1-33.
• [3] P. Billingsley, Probability and Measure, Wiley, New York-Chichester-Brisbane 1979.
• [4] S. Kwapień and W. A. Woyczyński, Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser, Boston, MA, 1992.
• [5] M. Maejima, V. Pérez-Abreu, and K. Sato, A class of multivariate infinitely divisible distributions related to arcsine density, Bernoulli 18 (2) (2012), pp. 476-495.
• [6] M. Maejima and K. Sato, Semi-Lévy processes, semi-selfsimilar additive processes, and semi-stationary Ornstein-Uhlenbeck type processes, J. Math. Kyoto Univ. 43 (3) (2003), pp. 609-639.
• [7] M. Maejima and K. Sato, The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions, Probab. Theory Related Fields 145 (1-2) (2009), pp. 119-142.
• [8] M. Maejima and Y. Ueda, Stochastic integral characterizations of semi-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes, Commun. Stoch. Anal. 3 (3) (2009), pp. 349-367.
• [9] A. Prékopa, On stochastic set functions. I, Acta Math. Acad. Sci. Hungar. 7 (1956), pp. 215-263.
• [10] A. Prékopa, On stochastic set functions. II, Acta Math. Acad. Sci. Hungar. 8 (1957), pp. 337-374.
• [11] A. Prékopa, On stochastic set functions. III, Acta Math. Acad. Sci. Hungar. 8 (1957), pp. 375-400.
• [12] B. S. Rajput and J. Rosiński, Spectral representations of infinitely divisible processes, Probab. Theory Related Fields 82 (3) (1989), pp. 451-487.
• [13] A. Rocha-Arteaga and K. Sato, Topics in Infinitely Divisible Distributions and Lévy Processes, Sociedad Matemática Mexicana, México 2003.
• [14] G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman, New York 1994.
• [15] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge 1999.
• [16] K. Sato, Stochastic integrals in additive processes and application to semi-Lévy processes, Osaka J. Math. 41 (1) (2004), pp. 211-236.
• [17] K. Sato, Additive processes and stochastic integrals, Illinois J. Math. 50 (1-4) (2006), pp. 825-851.
• [18] K. Sato, Two families of improper stochastic integrals with respect to Lévy processes, ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006), pp. 47-87.
• [19] K. Sato, Monotonicity and non-monotonicity of domains of stochastic integral operators, Probab. Math. Statist. 26 (1) (2006), pp. 23-39.
• [20] K. Sato, Transformations of infinitely divisible distributions via improper stochastic integrals, ALEA Lat. Am. J. Probab. Math. Stat. 3 (2007), pp.67-110.
• [21] K. Sato, Description of limits of ranges of iterations of stochastic integral mappings of infinitely divisible distributions, ALEA Lat. Am. J. Probab. Math. Stat. 8 (2011), pp. 1-17.
• [22] K. Sato, Inversions of infinitely divisible distributions and conjugates of stochastic integral mappings, J. Theoret. Probab. 26 (4) (2013), pp. 901-931.
• [23] K. Sato, Stochastic integrals with respect to Lévy processes and infinitely divisible distributions, Sugaku Expositions 27 (1) (2014), pp. 19-42.
• [24] K. Urbanik and W. A. Woyczyński, A random integral and Orlicz spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.15 (1967), pp. 161-169.

Identyfikatory

DOI

10.19195/0208-4147.39.1.14