A solution selection problem with small stable perturbations

Flandoli, Franco; Högele, Michael

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A solution selection problem with small stable perturbations

Franco Flandoli, Michael Högele

The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift.

Metadaten
Author details:	Franco Flandoli, Michael Högele GND
URN:	urn:nbn:de:kobv:517-opus-71205
ISSN:	2193-6943
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (3 (2014) 8)
Publisher:	Universitätsverlag Potsdam
Place of publishing:	Potsdam
Publication type:	Preprint
Language:	English
Year of first publication:	2014
Publication year:	2014
Publishing institution:	Universität Potsdam
Publishing institution:	Universitätsverlag Potsdam
Release date:	2014/07/16
Tag:	Peano phenomena; non-uniqueness; singular drifts; stochastic differential equations; zero-noise limit
Volume:	3
Issue:	8
Number of pages:	43
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:	34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Fxx Limit theorems [See also 28Dxx, 60B12] / 60F99 None of the above, but in this section
	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 / 60G51 Processes with independent increments; Lévy 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 / 60G52 Stable 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) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05]
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2014
Publishing method:	Universitätsverlag Potsdam
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz

A solution selection problem with small stable perturbations

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