Stochastic integration for operator valued processes on hilbert spaces and on nuclear spaces

Abstract

The representation of a nuclear space valued square integrable martingale by means of another nuclear space valued square integrable martingale is given in terms of stochastic inegrals of operator valued processes. The construction of the stochastic integral goes through that of operator valued processes on Hilbert spaces. A new approach is given for the Hilbertian case, so that only the integration of Hilbert-Schmidt operator valued processes is needed to represent square integrable martingales

Keywords:

• Stochastic integration
• Hilhert space valued square integrable martingales
• nuclear space valued square integrable martingales
• representation of square integrable martingales

^∗The research of H.K. was supported by AFOSR Contract No. F49620 82 C 0009

^∗The research of H.K. was supported by AFOSR Contract No. F49620 82 C 0009

Notes

^∗The research of H.K. was supported by AFOSR Contract No. F49620 82 C 0009