## Exact Statistics of Record Increments of Random Walks and Lévy Flights.

- Claude Godrèche, Satya N. Majumdar, Grégory Schehr
- Physical review letters
- 2016

@inproceedings{Barlevy2006CharacterizationsIA, title={Characterizations in a Random Record Model with a Nonidentically Distributed Initial Record}, author={Gadi Barlevy and H. N. Nagaraja}, year={2006} }

- Published 2006

We consider a sequence, of random length M , of independent, continuous observations Xi, 1 ≤ i ≤ M, where M is geometric, X1 has cumulative distribution function (CDF) G, and Xi, i ≥ 2, have CDF F . Let N be the number of upper records and let Rn, n ≥ 1, be the nth record value. We show that N is independent of F if and only if G(x) = G0(F (x)) for some CDF G0, and that if E(|X2|) is finite then so is E(|Rn|), n ≥ 2, whenever N ≥ n or N = n. We prove that the distribution of N , along with… CONTINUE READING