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Media type:
E-Article
Title:
Joint Continuity of the Intersection Local Times of Markov Processes
Contributor:
Rosen, Jay
imprint:
Institute of Mathematical Statistics, 1987
Published in:The Annals of Probability
Language:
English
ISSN:
0091-1798
Origination:
Footnote:
Description:
<p>We describe simple conditions on the transition density functions of two independent Markov processes X and Y which guarantee the existence of a continuous version for the intersection local time, formally given by α (z, H) = ∫<sub>H</sub>∫ δ<sub>z</sub>(Y<sub>t</sub>- X<sub>s</sub>) ds dt. In the analogous case of self-intersections α can be discontinuous at z = 0. We develop a Tanaka-like formula for α and use this to show that the singular part of α (z,[ 0, T]<sup>2</sup>) as z → 0 is given by 2∫<sup>T</sup>
<sub>0</sub>U(X<sub>t</sub>- z, X<sub>t</sub>) dt, a.s., where U is the 1-potential of X.</p>