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Contents of PMS, Vol. 27, Fasc. 1,
pages vy processes and stochastic integrals in Banach spaces - 75
 

LÉVY PROCESSES AND STOCHASTIC INTEGRALS IN BANACH SPACES

David Applebaum

Abstract: We review infinite divisibility and Lévy processes in Banach spaces and discuss the relationship with notions of type and cotype. The Lévy-Itô decomposition is described. Strong, weak and Pettis-style notions of stochastic integral are introduced and applied to construct generalised Ornstein-Uhlenbeck processes.

2000 AMS Mathematics Subject Classification: 60G51, 60BU, 60H05, 47B48.

Key words and phrases: Lévy process, Lévy measure, type, co-type, Lévy-Itô decomposition, stochastic integral, Ornstein-Uhlenbeck process.

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