Hidden regular variation for point processes and the single/multiple large point heuristic

Dombry, Clément; Tillier, Charles; Wintenberger, Olivier

doi:10.1214/21-aap1675

Cited by 3 publications

(2 citation statements)

References 32 publications

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“…Ap4) One advantage of treating RV with respect to some boundedness is that this approach includes naturally also the concept of hidden RV discussed for instance in [28,43,50]. Indeed, in our settings hidden RV corresponds to the choice of B F , with F ⊂ D closed being the boundedness on D F = D \ {F } defined in Section 2.2.…”

Section: Applications and Open Questionsmentioning

confidence: 99%

Tail measures and regular variation

Bladt

Hashorva

Shevchenko

2022

Electron. J. Probab.

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A general framework for the study of regular variation (RV) is that of Polish starshaped metric spaces, while recent developments in [41] have discussed RV with respect to a properly localised boundedness B. Along the lines of the latter approach, we discuss the RV of Borel measures and random processes on a general Polish metric spaces (D, dD). Tail measures introduced in [47] appear naturally as limiting measures of regularly varying time series. We define tail measures on the measurable space (D, D) indexed by H(D), a countable family of 1-homogeneous coordinate maps, and show some tractable instances for the investigation of RV when B is determined by H(D). This allows us to study the regular variation of càdlàg processes on D(R l , R d ) retrieving in particular results obtained in [59] for RV of stationary càdlàg processes on the real line removing l = 1 therein. Further, we discuss potential applications and open questions.

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Section: Applications and Open Questionsmentioning

confidence: 99%

Tail measures and regular variation

Bladt

Hashorva

Shevchenko

2022

Electron. J. Probab.

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“…In the particular case F = {a} we write simply B a and V a , respectively. The boundedness B F appears in connection with hidden regular variation, see e.g., [14,32], whereas B 0 is the common boundedness used in RV setup, see e.g., [9,13] and references therein.…”

Section: Boundedness On Polish Spaces and Boundedly-finite Measuresmentioning

confidence: 99%

Tail Measures and Regular Variation

Bladt,

Hashorva,

Shevchenko

2021

Preprint

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A general framework for the study of regular variation is that of Polish star-shaped metric spaces, while recent developments in [1] have discussed regular variation in relation to a boundedness and weaker assumptions are imposed therein on the structure of Polish space. Along the lines of the latter approach, we discuss the regular variation of measures and processes on Polish spaces with respect to some given boundedness. We then focus on regular variation of càdlàg processes on D(R l , R d ), which was recently studied for stationary càdlàg processes on the real line in [2]. Tail measures introduced in [3] appear naturally as limiting measures of regularly varying random processes, and we show that this continues to hold true in our general setting. We derive several results for tail measures and their local tail and spectral tail processes which are crucial for the investigation of regular variation of Borel measures.

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Foundation

Resnick

2024

The Art of Finding Hidden Risks

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Hidden regular variation for point processes and the single/multiple large point heuristic

Cited by 3 publications

References 32 publications

Tail measures and regular variation

Tail measures and regular variation

Tail Measures and Regular Variation

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