Some functional limit theorems for compound Cox processes

Journal Article · Wed Jun 08 00:00:00 EDT 2016 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4952004· OSTI ID:22608966

Korolev, Victor Yu. ^[1]; Chertok, A. V. ^[1]; Korchagin, A. Yu. ^[1]; Kossova, E. V. ^[2]; Zeifman, Alexander I. ^[3]

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1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation)
2. Higher School of Economics National Research University, Moscow (Russian Federation)
3. Vologda State University, S.Orlova, 6, Vologda (Russian Federation)

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.

• OSTI ID: 22608966
• Journal Information: AIP Conference Proceedings, Vol. 1738, Issue 1; Conference: ICNAAM 2015: International conference of numerical analysis and applied mathematics 2015, Rhodes (Greece), 22-28 Sep 2015; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CONVERGENCE
DISTRIBUTION
GRAPH THEORY
MATHEMATICAL SPACE
RANDOMNESS
STOCHASTIC PROCESSES