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Lévy processes and stochastic integrals in Banach spaces

Applebaum D.

Probability and Mathematical Statistics

2007

Vol. 27, Fasc. 1

75--88

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

The type and cotype of Calderon-Lozanovskij spaces

Cerda J., Mastyło M.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 2

105-117

We prove certain vector-valued continuous inclusions for Calderon-Lozanovskij spaces and, by interpolation, we obtain results on the type and cotype of these spaces. We also give an extension of Kwapień's result which states that, for [1 is less than or equal to p is less than or equal to 2], every operator from l[sub 1] into l[sub p] is (r,1)-summing, if 1/r=3/2 - 1/p.