On the location of the maximum of a process: Lévy, Gaussian and Random field cases

López, Sergio I.; Pimentel, Leandro P. R.

doi:10.1080/17442508.2018.1499103

Cited by 2 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [16] is proven that, for x and y fixed, the maximum is attained at a unique location with probability one. However, it is not true that this uniqueness holds simultaneously for all points x, y ∈ R × N. To see an example, for x > 0 define…”

Section: Convergence Of the Brownian Last-passage Percolation Systemmentioning

confidence: 99%

Attractiveness of Brownian queues in tandem

Cator

López

Pimentel³

2019

Queueing Syst

Self Cite

View full text Add to dashboard Cite

Consider a sequence of n bi-infinite and stationary Brownian queues in tandem. Assume that the arrival process entering in the first queue is a zero mean ergodic process. We prove that the departure process from the n-th queue converges in distribution to a Brownian motion as n goes to infinity. In particular this implies that the Brownian motion is an attractive invariant measure for the Brownian queueing operator. Our proof exploits the relationship between the Brownian queues in tandem and the last-passage Brownian percolation model, developing a coupling technique in the second setting. The result is also interpreted in the related context of Brownian particles acting under one sided reflection.

show abstract

Section: Convergence Of the Brownian Last-passage Percolation Systemmentioning

confidence: 99%

Attractiveness of Brownian queues in tandem

Cator

López

Pimentel³

2019

Queueing Syst

Self Cite

View full text Add to dashboard Cite

show abstract

“…The arguments used in these papers are all specific to proving uniqueness of the minimizer of a Gaussian process, rather than a more general function of a Gaussian process. In addition, Pimentel (2014) and López and Pimentel (2016) characterize uniqueness using differentiability of a perturbation-expectation operator, which is useful in some examples.…”

Section: The Argmin Theoremmentioning

confidence: 99%

Almost Sure Uniqueness of a Global Minimum Without Convexity

Cox¹

2018

Preprint

View full text Add to dashboard Cite

This paper establishes the argmin of a random objective function to be unique almost surely. This paper first formulates a general result that proves almost sure uniqueness without convexity of the objective function. The general result is then applied to a variety of applications in statistics. Four applications are discussed, including uniqueness of M-estimators, both classical likelihood and penalized likelihood estimators, and two applications of the argmin theorem, threshold regression and weak identification.

show abstract

On the location of the maximum of a process: Lévy, Gaussian and Random field cases

Cited by 2 publications

References 13 publications

Attractiveness of Brownian queues in tandem

Attractiveness of Brownian queues in tandem

Almost Sure Uniqueness of a Global Minimum Without Convexity

Contact Info

Product

Resources

About