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

  title={Stationary and multi-self-similar random fields with stochastic volatility},
  author={Almut E. D. Veraart},
  journal={Stochastics An International Journal of Probability and Stochastic Processes},
  pages={848 - 870}
  • Almut E. D. Veraart
  • Published 12 February 2014
  • Mathematics
  • Stochastics An International Journal of Probability and Stochastic Processes
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, two methods for parameterizing the weight functions in the MA representation are presented: one method is based on Fourier techniques and aims at reproducing a given correlation structure, the other… 
Volatility Modulated Volterra Processes
This chapter introduces the class of volatility modulated Volterra processes. We define these processes and discuss basic probabilistic properties with focus on the temporal dependency structure.
Mixing Properties of Multivariate Infinitely Divisible Random Fields
In this work we present different results concerning mixing properties of multivariate infinitely divisible (ID) stationary random fields. First, we derive some necessary and sufficient conditions
The Ambit Framework
This chapter contains an extensive introduction to fundamental concepts leading to the definition of ambit fields and processes. The theory of Levy bases is followed by concepts of stochastic


Self-Similarity and Lamperti Transformation for Random Fields
We define multi-self-similar random fields, that is, random fields that are self-similar component-wise. We characterize them, relate them to stationary random fields using a Lamperti-type
Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
Stable random variables on the real line Multivariate stable distributions Stable stochastic integrals Dependence structures of multivariate stable distributions Non-linear regression Complex stable
Extremes of regularly varying Lévy-driven mixed moving average processes
  • Vicky Fasen
  • Mathematics
    Advances in Applied Probability
  • 2005
In this paper, we study the extremal behavior of stationary mixed moving average processes of the form Y(t)=∫ℝ+×ℝ f(r,t-s) dΛ(r,s), t∈ℝ, where f is a deterministic function and Λ is an infinitely
Stable mixed moving averages
SummaryThe class of (non-Gaussian) stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise, leading to stable
Quasi Ornstein–Uhlenbeck processes
The question of existence and properties of stationary solutions to Langevin equations driven by noise processes with stationary increments is discussed, with particular focus on noise processes of
Ambit Processes and Stochastic Partial Differential Equations
Ambit processes are general stochastic processes based on stochastic integrals with respect to Levy bases. Due to their flexible structure, they have great potential for providing realistic models
Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency
Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an
Econometric analysis of realized volatility and its use in estimating stochastic volatility models
Summary. The availability of intraday data on the prices of speculative assets means that we can use quadratic variation‐like measures of activity in financial markets, called realized volatility, to