Law of large numbers for monotone convolution

• Autorzy: Wang J.-C. , Wendler E.
• Języki publikacji: EN

Abstrakty

EN

Using the martingale convergence theorem, we prove a law of large numbers for monotone convolutions μ₁ ◃ μ₂ ◃ . . . ◃ μ_n, where μ_j ’s are probability laws on R with finite variances but not required to be identical.

Słowa kluczowe

EN

monotone convolution; Markov chains; martingale; law of large numbers

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 225--231
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Wang J.-C.

• University of Saskatchewan, 106 Wiggins Road Saskatoon, SK S7N 5E6

autor

Wendler E.

• University of Saskatchewan, 106 Wiggins Road Saskatoon, SK S7N 5E6

Bibliografia

• [1] M. Anshelevich and J. D. Williams, Limit theorems for monotonic convolution and the Chernoff product formula, Int. Math. Res. Not. IMRN (2013). doi: 10.1093/imrn/rnt018.
• [2] U. Franz, Monotone and Boolean convolutions for non-compactly supported probability measures, Indiana Univ. Math. J. 58 (3) (2009), pp. 1151-1185.
• [3] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley Publishing Company, Cambridge 1954.
• [4] G. Letac and D. Malouche, The Markov chain associated to a Pick function, Probab. Theory Related Fields 118 (2000), pp. 439-454.
• [5] N. Muraki, Monotonic convolution and monotonic Lévy-Hinčin formula, preprint, 2000.
• [6] N. Muraki, The five independences as natural products, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6 (3) (2003), pp. 337-371.
• [7] R. Speicher, On universal products, in: Free Probability Theory, D. Voiculescu (Ed.), Fields Inst. Commun. 12, Amer. Math. Soc., 1997, pp. 257-266.
• [8] J.-C. Wang, Strict limit types for monotone convolution, J. Funct. Anal. 262 (1) (2012), pp. 35-58.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).