Abstracts
In this chapter the structure of the likelihood process (process of Radon-Nikodym derivatives) is derived when considering two probability measures on the canonical spaces W and M, assuming that one of the probabilities is locally absolutely continuous with respect to the other. Also, it is shown how to change measure using martingales or just local martingales.
It is important to understand the contents of Theorem 5.1.1, but not necessary to read the proof in detail. Also, Section 5.2 may be omitted on a first reading.
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Chapter 5
Boel, R., Varaiya, P. and Wong, E. (1975). Martingales on jump processes, Part I: Representation results, Part II: Applications. SIAM J. Control 13, 999–1061.
Doléans-Dade, C. (1970). Quelques applications de la formule de changement de variable pour les semimartingales. Z. Wahrsch. verw. Gebiete 16, 181–194.
Girsanov, I.V. (1960). On transforming a certain class of stochastic processes by absolutely continuous substitution of measures. Theory Probab. Appl. 5, 285–301.
Jacod, J. (1975). Multivariate point processes: Predictable projection, Radon-Nikodym derivatives, representation of martingales. Z. Wahrsch. verw. Gebiete 31, 235–253.
Jacod, J. and Mémin, J. (1976). Caractéristiques locales et conditions de continuité absolue pour les semi-martingales. Z. Wahrsch. verw. Gebiete 35, 1–37.
Jacod, J. and Shiryaev, A.N. (1987). Limit Theorems for Stochastic Processes. Springer, Berlin. 2nd edition (2003).
Kabanov, Y., Liptser, R.S. and Shiryaev, A.N. (1976). Criteria of absolute continuity of measures corresponding to multivariate point processes. In Proc. 3rd Japan-USSR Symposium on Probability. Lecture Notes in Mathematics 550, Springer, Berlin, 232–252.
Kabanov, Y., Liptser, R.S. and Shiryaev, A.N. (1977). On the question of absolute continuity and singularity of probability measures. Math. USSR Sb. 33, 203–221.
Kabanov, Y., Liptser, R.S. and Shiryaev, A.N. (1979,1980). Absolute continuity and singularity of locally absolutely continuous probability distributions I–II. Math. USSR Sb. 35, 631–680, ibid. 36, 31–58.
van Schuppen, J.H. and Wong, E. (1974). Transformations of local martingales under a change of law. Ann. Probab. 2, 879–888.
Segall, A. and Kailath, T. (1975). Radon-Nikodym derivatives withrespect to measures induced by discontinuous independent increment processes. Ann. Probab. 3, 449–464.
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© 2006 Birkhäuser Boston
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(2006). Likelihood Processes. In: Point Process Theory and Applications. Probability and its Applications. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4463-6_5
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DOI: https://doi.org/10.1007/0-8176-4463-6_5
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4215-0
Online ISBN: 978-0-8176-4463-5
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