On Maximum Increase and Decrease of Brownian Motion
Paavo Salminen, Pierre Vallois
Abstract
The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times of the infimum and the supremum before the exponential time. It is seen that an important element in our formula is the distribution of the maximum decrease for the three dimensional Bessel process with drift started from 0 and stopped at the first hitting of a given level. From the joint distribution of the maximum increase and decrease it is possible to calculate the correlation coefficient between these at a fixed time and this is seen to be -0.47936... .
Create a lesson
Related papers
Distribution-constrained optimal multiple stopping: the Root-type solution
Shuoqing Deng, Daxin Huang
Universality and sharp thresholds for ellipsoid fitting
Frederic Koehler, Youngtak Sohn
Local Laws and Edge Universality for Noncentral Sample Covariance Matrices
Can Hu, Jiang Hu, Zhidong Bai
Well-posedness and regularity of stochastic heat equations on moving domains
Chongyang Ren, Tusheng Zhang
Traveling Waves in Equity Markets with Rank-Based Entry and Exit
Graeme Baker, Caroline Smyth
An approximate zero bias transformation for random sums: Applications to sampling with outliers, auto insurance, and generative AI
Wasamon Jantai, Nathakhun Wiroonsri