Symmetric stable processes, Fubini’s theorem, and some extensions of the Ciesielski-Taylor identities in law. (English) Zbl 0831.60049

Donati-Martin, C.; Song, S.; Yor, M.

Stochastics Stochastics Rep. 50, No. 1-2, 1-33 (1994).

Summary: The Ciesielski-Taylor identities in law between certain functionals of two Bessel processes are generalized with the help of an integration by parts formula for squares of Gaussian processes. In turn, this formula may be extended to stable processes. In fact, an infinite-dimensional version of this formula characterizes stable processes.

MSC:

60G05	Foundations of stochastic processes
60G07	General theory of stochastic processes

Keywords:

Ciesielski-Taylor identities; Bessel processes; stable processes