Φ′-VALUED MARTINGALE MEASURES AND THEIR LIMIT THEOREMS^*

Abstract

This work is devoted to the study of martingale measures with values in the dual of a nuclear space and to the construction of stochastic integrals with respect to some classes of these processes. This permits us to establish calculus and we introduce the concept of convergence of Φ′-valued martingale measures in distribution. The conditions are given for convergence of Φ′-valued martingale measures.

^*This project is supported by the National Science Foundation of China (Project 19971072) and Qing-Lan Project of Jiangsu Province.

Keywords:

• Φ′-valued martingale measure
• Stochastic integral
• Representation theorem
• Limit theorem

Acknowledgments

Notes

^*This project is supported by the National Science Foundation of China (Project 19971072) and Qing-Lan Project of Jiangsu Province.