Lévy-based growth models

Jónsdóttir, Kristjana Ỷr; Schmiegel, Jürgen; Jensen, Eva B. Vedel

doi:10.3150/07-bej6130

Cited by 32 publications

(26 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using the tools of Lévy theory, it is possible to derive moment relations as shown in the present paper for the purely spatial case [35]. This approach to spatio-temporal modeling is expected to be very flexible and has been used with success in growth modeling [23] (see also [22]). It will be interesting to investigate how it performs compared to the earlier methods described in [6], [7], [8], and [14].…”

Section: A T (X) K((x T) (Y S))l(d(y S)) mentioning

confidence: 99%

Lévy-based Cox point processes

2008

View full text Add to dashboard Cite

In this paper we introduce Lévy-driven Cox point processes (LCPs) as Cox point processes with driving intensity function defined by a kernel smoothing of a Lévy basis (an independently scattered, infinitely divisible random measure). We also consider log Lévy-driven Cox point processes (LLCPs) with equal to the exponential of such a kernel smoothing. Special cases are shot noise Cox processes, log Gaussian Cox processes, and log shot noise Cox processes. We study the theoretical properties of Lévy-based Cox processes, including moment properties described by nth-order product densities, mixing properties, specification of inhomogeneity, and spatio-temporal extensions.

show abstract

Section: A T (X) K((x T) (Y S))l(d(y S)) mentioning

confidence: 99%

Lévy-based Cox point processes

2008

View full text Add to dashboard Cite

show abstract

“…Roughly speaking, an ambit field is a tempo-spatial random field which is defined as an integral over a random measure (a Lévy basis) where the integrand is a deterministic function times a stochastic volatility/intermittency field. Initially, tempo-spatial ambit fields and their null-spatial analogues were suggested as tools for modelling turbulence in physics (see Barndorff-Nielsen and Schmiegel [7,8]), but have also been successfully applied to model tumour growth [13].…”

Section: Introductionmentioning

confidence: 99%

Approximating ambit fields via Fourier methods

Eyjolfsson

2015

Stochastics

View full text Add to dashboard Cite

In their paper employ so called ambit fields to model electricity spot-forward dynamics. We briefly introduce and discuss ambit fields, and introduce a novel method for approximating general ambit fields by a linear combination of ambit fields driven by exponential kernel functions (as has already been done in the null-spatial case of Lévy semistationary processes by Benth et al. [11]) by approximating the deterministic kernel function by a carefully selected finite sum. Moreover, we shall study examples, in the setting of modelling electricity forward markets, of ambit fields with singular kernel functions to illustrate the usefulness of our method for pricing purposes.

show abstract

“…In relation to variance estimation, Lévy-based models have earlier been used in circular systematic sampling (Jónsdóttir et al, 2013a). Lévy-based models have also been shown to be a useful modelling tool for Cox point processes and growth (Hellmund et al, 2008;Jónsdóttir et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

Estimation of Sample Spacing in Stochastic Processes

Rønn-Nielsen¹,

Sporring²,

Hahn³

2017

Image Anal Stereol

View full text Add to dashboard Cite

Motivated by applications in electron microscopy, we study the situation where a stationary and isotropic random field is observed on two parallel planes with unknown distance. We propose an estimator for this distance. Under the tractable, yet flexible class of Lévy-based random field models, we derive an approximate variance of the estimator. The estimator and the approximate variance perform well in two simulation studies.

show abstract

Lévy-based growth models

Cited by 32 publications

References 44 publications

Lévy-based Cox point processes

Lévy-based Cox point processes

Approximating ambit fields via Fourier methods

Estimation of Sample Spacing in Stochastic Processes

Contact Info

Product

Resources

About