Extremes of independent Gaussian processes

By Zakhar Kabluchko. 2009

64 citations recorded by the source corpus.

For every n ∈ ℕ, let X1n,..., Xnn be independent copies of a zero-mean Gaussian process Xn = {Xn(t), t ∈ T}. We describe all processes which can be obtained as limits, as n→ ∞, of the process an(Mn − bn), where Mn(t) =  maxi = 1,...,nXin(t), and an, bn are normalizing constants. We also provide an analogous characterization for the limits of the process anLn, where Ln(t) =  min i = 1,...,n |Xin(t)|.

Subfields: Artificial Intelligence, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9b1bde69f2aa346a07f3609f13799d8afd1b7765

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Sebastian Engelke
2. A. C. Davison
3. Peiman Asadi
4. Claudia Klüppelberg
5. Richard A. Davis
6. Martin Schlather
7. C. Steinkohl
8. Dimitris Nicolas Politis

In Finance

1. A. C. Davison
2. Sebastian Engelke
3. Raphaël Huser
4. Emeric Thibaud
5. Claudia Klüppelberg
6. Peiman Asadi
7. C. Steinkohl
8. Zakhar Kabluchko

In Mathematical Physics

1. A. C. Davison
2. Sebastian Engelke
3. Martin Schlather
4. Richard A. Davis
5. Peiman Asadi
6. Zakhar Kabluchko
7. Claudia Klüppelberg
8. C. Steinkohl

Citations in the corpus

• Efficient inference and simulation for elliptical Pareto processes (2013, unknown): “…function ρα depends on α such that the limit γ(s2 − s1) = limα→∞ α{1 − ρα(s1, s2)} exists and satisfies 0 < γ(s2 − s1) < ∞ for all sites s1, s2 with s1 6= s2, the extremal-t process Z∗ converges to Z∗BR as α tends to infinity (Nikoloulopoulos et al., 2009; Kabluchko, 2011; Engelke et al., 2012).”
• Estimation of Hüsler–Reiss distributions and Brown–Resnick processes (2012, background): “Kabluchko, M. Schlather Table 1. Estimation results. The values for the standard deviation are obtained from simulating and re-estimating the respective models 100 times. estimator α s β c θ̂PROJ, LS 0.296 (0.0193) 0.234 (0.0744) 0.379 (0.532) 1.67 (0.1761) θ̂SPEC 0.338 (0.0166) 0.687 (0.1797) 0.456”
• Statistical inference for max‐stable processes in space and time (2012, background): “It can also be derived from theorem 2 together with theorem 6 in Kabluchko (2011).”
• Extremes on river networks (2015, methodology): “, ηΓ(tm)) is max-stable and its exponent measure VΓ,t defined in (5) is characterized by [Kabluchko (2011)]”