LÉVY PROCESSES AND STOCHASTIC INTEGRALS IN BANACH SPACES
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.