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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?...

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    $\begingroup$ Perhaps local times? $\endgroup$
    – Bati
    Apr 14, 2014 at 12:40
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    $\begingroup$ 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. $\endgroup$ Apr 14, 2014 at 13:21
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    $\begingroup$ 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. $\endgroup$ Apr 14, 2014 at 13:25
  • $\begingroup$ How do I prove that it hits immediately infinitely many times just after hitting once? $\endgroup$
    – Gaurav
    Apr 14, 2014 at 16:28
  • $\begingroup$ @Bati No local times can be calculated it seems..... I wanted to know number of times $\endgroup$
    – Gaurav
    Apr 14, 2014 at 17:01

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