Abstract
In [1], Dynkin gave a very simple proof of Nagasawa s theorem (see [3] or [4]) and its generalization [2]. His proof is based on a simple general result on measurable flows (see [1], Theorems 1 and 2). Unfortunately in the application to Nagasawa’s theorem in section 3, there is a measurability difficulty. This is hinted at in the footnote on page 616 of [1]. The purpose of this note is to correct this difficulty and to prove a theorem that shows that there really is a measurability problem that must be addressed. We use the notation of [1] without special mention.
Research supported, in part, by NSF Grant DMS 8919377
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
E. B. Dynkin. An application of flows to time shift and time reversal in stochastic processes. Trans. Amer. Math. Soc. 287 (1985), 613–619.
R. K. Getoor and J. Glover. Riesz decompositions in Markov process theory. Trans. Amer. Math. Soc. 285 (1984), 107–132.
R. K. Getoor and M. J. Sharpe. Naturality, standardness, and weak duality for Markov processes. Z. Wahrscheinlichkeitstheorie verw. Geb. 67 (1984), 1–62.
M. J. Sharpe. Some transformations of diffusions by time reversal. Ann. Prob. 8 (1980), 1157–1162.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Birkhäuser Boston, Inc.
About this chapter
Cite this chapter
Getoor, R.K. (1986). Some Remarks on a Theorem of Dynkin. In: Çinlar, E., Chung, K.L., Getoor, R.K., Glover, J. (eds) Seminar on Stochastic Processes, 1985. Progress in Probability and Statistics, vol 12. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6748-2_6
Download citation
DOI: https://doi.org/10.1007/978-1-4684-6748-2_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4684-6750-5
Online ISBN: 978-1-4684-6748-2
eBook Packages: Springer Book Archive