Convoluted Brownian motion

  • In this paper we analyse semimartingale properties of a class of Gaussian periodic processes, called convoluted Brownian motions, obtained by convolution between a deterministic function and a Brownian motion. A classical example in this class is the periodic Ornstein-Uhlenbeck process. We compute their characteristics and show that in general, they are neither Markovian nor satisfy a time-Markov field property. Nevertheless, by enlargement of filtration and/or addition of a one-dimensional component, one can in some case recover the Markovianity. We treat exhaustively the case of the bidimensional trigonometric convoluted Brownian motion and the higher-dimensional monomial convoluted Brownian motion.

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Metadaten
Author details:Sylvie RoellyGND, Pierre Vallois
URN:urn:nbn:de:kobv:517-opus4-96339
ISSN:2193-6943
Subtitle (English):a semimartingale approach
Publication series (Volume number):Preprints des Instituts für Mathematik der Universität Potsdam (5 (2016) 9)
Publisher:Universitätsverlag Potsdam
Place of publishing:Potsdam
Publication type:Preprint
Language:English
Year of first publication:2016
Publication year:2016
Publishing institution:Universität Potsdam
Publishing institution:Universitätsverlag Potsdam
Release date:2016/09/23
Tag:Markov-field property; enlargement of filtration; periodic Gaussian process; periodic Ornstein-Uhlenbeck process
Volume:5
Issue:9
Number of pages:37
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G10 Stationary processes
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G15 Gaussian processes
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G17 Sample path properties
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05]
Publishing method:Universitätsverlag Potsdam
Collection(s):Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2016
License (German):License LogoKeine öffentliche Lizenz: Unter Urheberrechtsschutz
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