Abstract
| Original language | English |
|---|---|
| Journal | Journal of Applied Probability |
| Volume | 54 |
| Issue number | 3 |
| Pages (from-to) | 833-851 |
| ISSN | 0021-9002 |
| DOIs | |
| Publication status | Published - 2017 |
Keywords
- Convolution equivalence
- Excursion set
- Infinite divisibility
- Lévy-based modelling
Cite this
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Excursion Sets of Infinitely Divisble Random Fields with Convolution Equivalent Lévy Measure. / Rønn-Nielsen, Anders ; Jensen, Eva B. Vedel.
In: Journal of Applied Probability, Vol. 54, No. 3, 2017, p. 833-851.Research output: Contribution to journal › Journal article › Research › peer-review
TY - JOUR
T1 - Excursion Sets of Infinitely Divisble Random Fields with Convolution Equivalent Lévy Measure
AU - Rønn-Nielsen, Anders
AU - Jensen, Eva B. Vedel
PY - 2017
Y1 - 2017
N2 - We consider a continuous, infinitely divisible random field in ℝ d , d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields, we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.
AB - We consider a continuous, infinitely divisible random field in ℝ d , d = 1, 2, 3, given as an integral of a kernel function with respect to a Lévy basis with convolution equivalent Lévy measure. For a large class of such random fields, we compute the asymptotic probability that the excursion set at level x contains some rotation of an object with fixed radius as x → ∞. Our main result is that the asymptotic probability is equivalent to the right tail of the underlying Lévy measure.
KW - Convolution equivalence
KW - Excursion set
KW - Infinite divisibility
KW - Lévy-based modelling
KW - Convolution equivalence
KW - Excursion set
KW - Infinite divisibility
KW - Lévy-based modelling
UR - https://sfx-45cbs.hosted.exlibrisgroup.com/45cbs?url_ver=Z39.88-2004&url_ctx_fmt=info:ofi/fmt:kev:mtx:ctx&ctx_enc=info:ofi/enc:UTF-8&ctx_ver=Z39.88-2004&rfr_id=info:sid/sfxit.com:azlist&sfx.ignore_date_threshold=1&rft.object_id=954921347249
U2 - 10.1017/jpr.2017.37
DO - 10.1017/jpr.2017.37
M3 - Journal article
VL - 54
SP - 833
EP - 851
JO - Journal of Applied Probability
JF - Journal of Applied Probability
SN - 0021-9002
IS - 3
ER -