Conditional exponential moments for iterated Wiener integrals. (English) Zbl 0961.60053

Lyons, Terry; Zeitouni, Ofer

Ann. Probab. 27, No. 4, 1738-1749 (1999).

Authors’ summary: We provide sharp exponential moment bounds for (Stratonovich) iterated stochastic integrals under conditioning by certain small balls, including balls in certain Hölder-like norms of exponent greater than 1/3. The proof uses a control of the variation of the Lévy area, under conditioning. The results are applied to the computation of the Onsager-Machlup functional of diffusion processes with constant diffusion matrix.

Reviewer: Tomasz Bojdecki (Warszawa)

MSC:

60H05	Stochastic integrals
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60	Diffusion processes

Keywords:

iterated Wiener integrals; Lévy area; Onsager-Machlup functional