Name
Abstract | ||
|---|---|---|
We provide upper and lower bounds for the mean M(H) of sup(t >= 0) {B-H(t)- t}, with B-H(.) a zero-mean, variance-normalized version of fractional Brownian motion with Hurst parameter H is an element of (0, 1). We find bounds in (semi-) closed form, distinguishing between H is an element of (0, 1/2] and H is an element of [1/2, 1), where in the former regime a numerical procedure is presented that drastically reduces the upper bound. For H is an element of (0, 1/2], the ratio between the upper and lower bound is bounded, whereas for H is an element of [1/2, 1) the derived upper and lower bound have a strongly similar shape. We also derive a new upper bound for the mean of sup(t is an element of[0,1]) B-H(t), H is an element of (0, 1/2], which is tight around H = 1/2. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1017/jpr.2020.98 | JOURNAL OF APPLIED PROBABILITY |
Keywords | DocType | Volume |
Fractional Brownian motion, extreme value, bounds | Journal | 58 |
Issue | ISSN | Citations |
2 | 0021-9002 | 1 |
PageRank | References | Authors |
0.39 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bisewski Krzysztof | 1 | 1 | 0.39 |
| Dębicki Krzysztof | 2 | 1 | 0.39 |
| Michel Mandjes | 3 | 534 | 73.65 |