Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency

• Autorzy: Ole E. Barndorff-Nielsen , Fred Espen Benth , Almut E. D. Veraart
• Języki publikacji: EN

Abstrakty

EN

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 overview of the main findings in ambit stochastics up to date and establishes new results on general properties of ambit fields. Moreover, it develops the concept of tempo-spatial stochastic volatility/intermittency within ambit fields. Various types of volatility modulation ranging from stochastic scaling of the amplitude, to stochastic time change and extended subordination of random measures and to probability and Lévy mixing of volatility/intensity parameters will be developed. Important examples for concrete model specifications within the class of ambit fields are given.

Kategorie tematyczne

• 60G60: Random fields
• 60G10: Stationary processes
• 60G51: Processes with independent increments; L\'evy processes
• 60G57: Random measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 104
• Numer: 1
• Strony: 25-60

Daty

wydano

2015

Twórcy

autor

Ole E. Barndorff-Nielsen

• Thiele Center, Department of Mathematics, Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark

autor

Fred Espen Benth

• Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway

autor

Almut E. D. Veraart

• Department of Mathematics, Imperial College London, 180 Queen's Gate, SW7 2AZ London, UK

Identyfikatory

DOI

10.4064/bc104-0-2