Book ChapterDOI
Subordinated Processes with Infinite Variance
Aleksandra Grzesiek,Agnieszka Wyłomańska +1 more
- pp 111-135
TLDR
In this paper, three models of subordinated processes, namely, the gamma subordinator, the alpha-stable and the gamma sub-process, are considered and a simulation procedure is proposed to estimate the tail index of the external process.Abstract:
In this paper we consider three models of subordinated processes. A subordinated process, called also a time-changed process, is defined as a superposition of two independent stochastic processes. To construct such stochastic system we replace the time of a given process (called also an external process) by another process which becomes the “operational time”. In the literature one can find different models that are constructed as a superposition of two stochastic processes. The most classical example is the Laplace motion, also known as variance gamma process, is stated as a Brownian motion time-changed by the gamma subordinator. In this paper the considered systems are constructed by replacing the time of the symmetric \(\alpha \)-stable Levy motion with another stochastic process, namely the \(\alpha _S\)-stable, tempered \(\alpha _T\)-stable and gamma subordinator. We discuss the main characteristics of each introduced processes. We examine the characteristic function, the codifference, the probability density function, asymptotic tail behaviour and the fractional order moments. To make the application of these processes possible we propose a simulation procedure. Finally, we demonstrate how to estimate the tail index of the external process, i.e. alpha-stable Levy motion and by using Monte Carlo method we show the efficiency of the proposed estimation method.read more
Citations
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Journal ArticleDOI
Harmonic Analysis and the Theory of Probability. By S. Bochner pp. 176. 35s. 1955. (California University Press and Cambridge University Press)
Journal ArticleDOI
Linnik Lévy process and some extensions
TL;DR: In this paper, the Linnik Levy process (LLP) is proposed to model leptokurtic data with heavy-tailed behavior, and the authors give a step-by-step procedure of the parameters estimation and calibrate the parameters of the LLP with the Arconic Inc equity data taken from Yahoo finance.
DissertationDOI
Stochastic modeling and statistical properties of the Limit Order Book
TL;DR: This work ist eingereicht an der Technischen Universität Wien Fakultät für Mathematik and Geoinformation von MSc Dragana Radojičić Matrikelnummer: 11727238.
References
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BookDOI
Financial modelling with jump processes
Rama Cont,Peter Tankov +1 more
TL;DR: In this article, the authors provide a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists.
MonographDOI
Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
TL;DR: In this paper, the authors introduce sample path properties such as boundedness, continuity, and oscillations, as well as integrability, and absolute continuity of the path in the real line.
Journal ArticleDOI
The Variance Gamma Process and Option Pricing
TL;DR: In this article, a three-parameter stochastic process, termed the variance gamma process, is developed as a model for the dynamics of log stock prices, which is obtained by evaluating Brownian motion with drift at a random time given by a gamma process.
Book
Signal processing with alpha-stable distributions and applications
Chrysostomos L. Nikias,Min Shao +1 more
TL;DR: The Stable Distribution Symmetric Stable Random Processes Covariation and Conditional Expectation Parameter Estimates for Stable Distributions Estimation of Covariations Parametric Models of Stable Processes Linear Theory of Stability Processes as discussed by the authors.
Journal ArticleDOI
Long-range anticorrelations and non-Gaussian behavior of the heartbeat
Chung-Kang Peng,Chung-Kang Peng,Chung-Kang Peng,J. Mietus,J. Mietus,J. Mietus,Jeffrey M. Hausdorff,Jeffrey M. Hausdorff,Jeffrey M. Hausdorff,Shlomo Havlin,Shlomo Havlin,Shlomo Havlin,H. E. Stanley,H. E. Stanley,H. E. Stanley,Ary L. Goldberger,Ary L. Goldberger,Ary L. Goldberger +17 more
TL;DR: It is found that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range anticorrelations (up to 10(4) heart beats), and the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat.