Covariance of the running range of a Brownian trajectory
arXiv:1902.06963 · doi:10.1088/1751-8121/ab306c
Abstract
The question how the extremal values of a stochastic process achieved on different time intervals are correlated to each other has been discussed within the last few years on examples of the running maximum of a Brownian motion, of a Brownian Bridge and of a Slepian process. Here, we focus on the two-time correlations of the running range of Brownian motion - the maximal extent of a Brownian trajectory on a finite time interval. We calculate exactly the covariance function of the running range and analyse its asymptotic behaviour. Our analysis reveals non-trivial correlations between the value of the largest descent (rise) of a BM from the top to a bottom on some time interval, and the value of this property on a larger time interval.
arXiv comment13 pages, 3 figures
References in corpus (15)
- First-passage times in complex scale-invariant media
- Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
- Survival of an evasive prey
- Group Chase and Escape
- Record statistics for biased random walks, with an application to financial data
- Group chasing tactics: how to catch a faster prey?
- Towards a full quantitative description of single-molecule reaction kinetics in biological cells
- Survival probability of a particle in a sea of mobile traps: A tale of tails
- Sample-size dependence of the ground-state energy in a one-dimensional localization problem
- Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder
- Temporal correlations of the running maximum of a Brownian trajectory
- An exactly solvable record model for rainfall
- Universality classes of foraging with resource renewal
- Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model
- Optimally Frugal Foraging