Convoluted Brownian motion : a semimartingale approach

Roelly, Sylvie; Vallois, Pierre

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.

Metadaten
Author details:	Sylvie Roelly GND, 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):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz

Convoluted Brownian motion

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