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April, 1992 Multiple Points of Sample Paths of Markov Processes
Narn-Rueih Shieh
Ann. Probab. 20(2): 553-562 (April, 1992). DOI: 10.1214/aop/1176989790


We show that certain $d$-dimensional Markov processes $X(t), t\geq 0$, have the property that if $E$ is a closed subset of $R_+$ with sufficiently large Hausdorff dimension, then $X(E)$ has $k$-multiple points. This is applied directly to diffusions driven by stochastic differential equations and Levy processes with positive lower indices, solving problems posed by J. P. Kahane and S. J. Taylor.


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Narn-Rueih Shieh. "Multiple Points of Sample Paths of Markov Processes." Ann. Probab. 20 (2) 553 - 562, April, 1992.


Published: April, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0753.60036
MathSciNet: MR1159558
Digital Object Identifier: 10.1214/aop/1176989790

Primary: 60G17

Keywords: $k$-multiple points , Diffusions , Hausdorff measures , Levy processes

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 2 • April, 1992
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