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Ornstein–Uhlenbeck type processes with non-normal distribution

Part of: Stochastic processes Inference from stochastic processes Applications

Published online by Cambridge University Press:  14 July 2016

Jens Ledet Jensen  and
Jan Pedersen
Jens Ledet Jensen*
Affiliation:
University of Aarhus
Jan Pedersen*
Affiliation:
University of Aarhus
*
∗Postal address: Department of Theoretical Statistics, Institute of Mathematics, Ny Munkegade, DK-8000 Aarhus C, Denmark.
∗Postal address: Department of Theoretical Statistics, Institute of Mathematics, Ny Munkegade, DK-8000 Aarhus C, Denmark.
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Abstract

We analyse a class of diffusion models that (i) allows an explicit expression for the likelihood function of discrete time observation, (ii) allows the possibility of heavy-tailed observations, and (iii) allows an analysis of the tails of the increments. The class simply consists of transformed Ornstein–Uhlenbeck processes and is of relevance for heavy-tailed time series. We also treat the question of the existence of an equivalent martingale measure for the class of models considered.

Keywords

Distribution of incrementsequivalent martingale measureheavy tailslikelihood functionOrnstein–Uhlenbeck process

MSC classification

Primary: 60G10: Stationary processes
Secondary: 62M05: Markov processes 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 389 - 402
Copyright
Copyright © Applied Probability Trust 1999 

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