Stationary and multi-self-similar random fields with stochastic volatility

• Published in: Stochastics (Abingdon, Eng. : 2005) Vol. 87; no. 5; pp. 848 - 870
• Main Author: Veraart, Almut E.D.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.09.2015; Taylor & Francis Ltd
• Subjects: AMS Subject Classification: 60G10; Construction; Fields (mathematics); Fourier analysis; generalized Lamperti transform; infinite divisibility; Lévy basis; mixed moving average fields; multi-self-similarity; Representations; stationarity; Stochastic processes; stochastic volatility; Stochasticity; Transforms; type G distribution; Volatility; Weight function

This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average (MA) fields and their probabilistic properties are discussed. Also,...