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Change of measure up to a random time: theory

Published online by Cambridge University Press:  14 July 2016

T. M. Mortimer  and
David Williams
T. M. Mortimer
Affiliation:
University of Cambridge
David Williams*
Affiliation:
University of Cambridge
*
∗ Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, UK.
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Abstract

Change of measure up to fixed times or stopping times is the theme of the famous Cameron–Martin–Girsanov formula. The paper studies change of measure up to random times which are not stopping times of the natural filtration. The ultimate aim is to build up a family of interesting models for physics and chemistry.

Keywords

CONDITIONINGCAMERON–MARTIN–GIRSANOV FORMULAMARTINGALEDOOB TRANSFORM
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 914 - 918
Copyright
Copyright © Applied Probability Trust 1991 

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References

[1] Barlow, M. T. (1978) Study of a filtration expanded to include an honest time. Z. Wahrscheinlichkeitsth. 44, 307–323.10.1007/BF01013194Google Scholar
[2] Jeulin, T. (1980) Semimartingales et Grossissements d'une Filtration. Lecture Notes in Mathematics 833, Springer-Verlag, Berlin.10.1007/BFb0093539Google Scholar
[3] Jeulin, T. and Yor, M., (eds) (1985) Grossissements de Filtrations: Exemples et Applications. Lecture Notes in Mathematics 1118, Springer-Verlag, Berlin.10.1007/BFb0075765Google Scholar
[4] Mortimer, T. M. Change of measure up to a random time: applications and criticality (to appear).Google Scholar
[5] Rogers, L. C. G. and Williams, D. (1987) Diffusions, Markov Processes, and Martingales, 2: Ito Calculus. Wiley, Chichester.Google Scholar
[6] Westwater, J. (1980) On Edwards' model for long polymer chains. Comm. Math. Phys. 72, 131–174.10.1007/BF01197632Google Scholar
[7] Williams, D. (1979) Diffusions, Markov Processes, and Martingales, 1: Foundations. Wiley, Chichester.Google Scholar