Innovation projections of a jump process and local martingales
- 1 January 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 81 (1) , 77-90
- https://doi.org/10.1017/s0305004100000281
Abstract
Square integrable and local martingales on a family of σ-fields generated by a basic jump process are shown to have representations as stochastic integrals with respect to a family of martingales associated with the jump process by using the idea of an innovation projection and the associated Lévy system, which is a local characterization of the jumps.Keywords
This publication has 3 references indexed in Scilit:
- The Representation of Martingales of Jump ProcessesSIAM Journal on Control and Optimization, 1976
- The Representation of Functionals of Brownian Motion by Stochastic IntegralsThe Annals of Mathematical Statistics, 1970
- On Square Integrable MartingalesNagoya Mathematical Journal, 1967