An Increasing Diffusion
In , E. Çinlar and J. Jacod consider, among other things, the problem of whether every continuous strong Markov process of bounded variation is deterministic (a problem apparently also posed by S. Orey). They show that this question is equivalent to that of whether every strong Markov process satisfying an ODE X t ’ = F(Xt) is deterministic. At the time of writing , they thought they had a proof that this was indeed the case. They later found an error in this proof, but subsequently established the result in the case that (Xt) is one-dimensional. More formally, they can show the following.
KeywordsBrownian Motion Bounded Variation Monotone Convergence Unit Slope Cantelli Lemma
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- 2.E. Çinlar and J.Jacod. Representations of semi martingale Markov processes in terms of Wiener processes and Poisson random measures. Seminar on Stochastic Processes 1981, pp. 159–242. Birkhäuser, Boston, 1981.Google Scholar