Name
Abstract | ||
|---|---|---|
Let W = {W-n : n is an element of N} be a sequence of random vectors in R-d, d >= 1. In this paper we consider the logarithmic asymptotics of the extremes of W, that is, for any vector q > 0 in R-d, we find that log P(there exists n is an element of N: W-n > uq) as u -> infinity. We follow the approach of the restricted large deviation principle introduced in Duffy (2003). That is, we assume that, for every q >= 0, and some scalings {a(n)}, {v(n)}, (1/v(n)) log P(W-n/a(n) >= uq) has a, continuous in q, limit Jw(q). We allow the scalings {a(n)} and {v(n)} to be regularly varying with a positive index. This approach is general enough to incorporate sequences W, such that the probability law of W-n/a(n) satisfies the large deviation principle with continuous, not necessarily convex, rate functions. The equations for these asymptotics are in agreement with the literature. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1239/jap/1429282607 | JOURNAL OF APPLIED PROBABILITY |
Keywords | Field | DocType |
Extrema of stochastic process, large deviation theory | Combinatorics,Nonlinear system,Regular polygon,Large deviations theory,Logarithm,Statistics,Asymptotic analysis,Rate function,Mathematics | Journal |
Volume | Issue | ISSN |
52 | 1 | 0021-9002 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| K. M. Kosiński | 1 | 17 | 2.32 |
| Michel Mandjes | 2 | 534 | 73.65 |