Book ChapterDOI
Stationary processes of ornstein-uhlenbeck type
Ken-iti Sato,Makoto Yamazato +1 more
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This article is published in Lecture Notes in Mathematics.The article was published on 1983-01-01. It has received 81 citations till now. The article focuses on the topics: Ornstein–Uhlenbeck process & Stationary process.read more
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Book
Lévy Processes and Stochastic Calculus
TL;DR: In this paper, the authors present a general theory of Levy processes and a stochastic calculus for Levy processes in a direct and accessible way, including necessary and sufficient conditions for Levy process to have finite moments.
Journal ArticleDOI
Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics
TL;DR: The authors construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive Ornstein-Uhlenbeck (OU) processes, and study these models in relation to financial data and theory.
The Generalized Hyperbolic Model: Estimation, Financial Derivatives, and Risk Measures
TL;DR: In this article, the authors describe more realistic models for financial assets based on generalized hyperbolic (GH) distributions and their subclasses, which allow for a natural definiton of volatility models by replacing the mixing generalized inverse Gaussian (GIG) distribution by appropriate volatility processes.
Posted Content
Modelling by Lévy Processes for Financial Econometrics
TL;DR: In this article, the use of positive Ornstein-Uhlenbeck (OU) type processes inside stochastic volatility processes is discussed in some detail, and the basic probability theory asso-ciated with such models is discussed.
Journal ArticleDOI
Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
Ken-iti Sato,Makoto Yamazato +1 more
TL;DR: In this article, the class of limit distributions of Ornstein-Uhlenbeck processes on R d is characterized, and integro-differential equations for operator-self-decomposable distributions are established.
References
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Journal ArticleDOI
Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
Ken-iti Sato,Makoto Yamazato +1 more
TL;DR: In this article, the class of limit distributions of Ornstein-Uhlenbeck processes on R d is characterized, and integro-differential equations for operator-self-decomposable distributions are established.
Journal ArticleDOI
On a continuous analogue of the stochastic difference equation Xn=ρXn-1+Bn
TL;DR: The main analytical tool used to obtain these results is a theorem of Lukacs concerning characteristic functions of certain stochastic integrals as mentioned in this paper, and several other related results are obtained.
Journal ArticleDOI
An integral representation for selfdecomposable banach space valued random variables
Zbigniew J. Jurek,Wim Vervaat +1 more
Journal ArticleDOI
Class L of multivariate distributions and its subclasses
TL;DR: For any class Q of distributions on Rd, let L(Q) be the class of limit distributions of bn−1(X1 + … + Xn) − an, where {Xn} are independent Rd-valued random variables, each with distribution in Q, bn > 0, an ∈ Rd, and {bn−1Xj} is a null array as discussed by the authors.
Related Papers (5)
Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
Ken-iti Sato,Makoto Yamazato +1 more