S-transform and Hermite transform of Hilbert space-valued stochastic distributions with applications to stochastic differential equations

Abstract

The S-transform and the Hermite transform are defined on spaces of generalized stochastic distributions with values in a separable Hilbert space H. The applications to a stochastic differential equation in H are considered.

Keywords:

• S-transform
• Hermite transform
• stochastic distributions
• Cauchy problem
• white noise

AMS Subject Classification :

• 46F12
• 33C45
• 44A05
• 47D06

Acknowledgements

The work was supported by RFBR No 10-0196003p and the Programme of Ministry of Education of Russian Federation No. 2.1.1/2000.