On the time to reach maximum for a variety of constrained Brownian motions

Details On the time to reach maximum for a variety of constrained Brownian motions On the time to reach maximum for a variety of constrained Brownian motions

2008-02-19

arxiv.org/abs/0802.2619v1

Journal of Physics A Mathematical and Theoretical 41 (2008) 365005

Physics

Condensed Matter

Statistical Mechanics

Submitted to J. Phys. A

Scientific paper

10.1088/1751-8113/41/36/365005

We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit results for excursions, meanders and reflected bridges associated with Brownian motion. By subsequently integrating over M, the marginal density P(t_m) is obtained in each case in the form of a doubly infinite series. For the excursion and meander, we analyse the moments and asymptotic limits of P(t_m) in some detail and show that the theoretical results are in excellent accord with numerical simulations. Our primary method of derivation is based on a path integral technique; however, an alternative approach is also outlined which is founded on certain "agreement formulae" that are encountered more generally in probabilistic studies of Brownian motion processes.

Affiliated with

Also associated with

No associations

Rating

On the time to reach maximum for a variety of constrained Brownian motions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the time to reach maximum for a variety of constrained Brownian motions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the time to reach maximum for a variety of constrained Brownian motions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-338464