Any experts here please direct me to some appropriate keywords that I can search for. Consider a Brownian motion constrained to an upper and lower boundaries. Let's say I want to know that how many times it hits one of the two boundaries (let's say per unit time starting from stationary induced measure). How do I approach this problems?...
$\begingroup$
$\endgroup$
5
-
1$\begingroup$ Perhaps local times? $\endgroup$– BatiCommented Apr 14, 2014 at 12:40
-
3$\begingroup$ As soon as it hits the boundary once, it immediately hits it infinitely many more times. So either the answer is just infinity or "how many" is not the right question. $\endgroup$– Nate EldredgeCommented Apr 14, 2014 at 13:21
-
1$\begingroup$ This assumes that by "constrained" you mean "reflected at both boundaries". If you mean "conditioned to remain in the interval" then the answer is 0. $\endgroup$– Nate EldredgeCommented Apr 14, 2014 at 13:25
-
$\begingroup$ How do I prove that it hits immediately infinitely many times just after hitting once? $\endgroup$– GauravCommented Apr 14, 2014 at 16:28
-
$\begingroup$ @Bati No local times can be calculated it seems..... I wanted to know number of times $\endgroup$– GauravCommented Apr 14, 2014 at 17:01
Add a comment
|