Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Weak convergence of obliquely reflected diffusions

Andrey Sarantsev

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Abstract

Burdzy and Chen (Electron. J. Probab. 3 (1998) 29–33) proved results on weak convergence of multidimensional normally reflected Brownian motions. We generalize their work by considering obliquely reflected diffusion processes. We require weak convergence of domains, which is stronger than convergence in Wijsman topology, but weaker than convergence in Hausdorff topology.

Résumé

Burdzy et Chen (Electron. J. Probab. 3 (1998) 29–33) ont montré des résultats portant sur la convergence faible des mouvements Browniens multidimensionnels avec réflexion normale. Nous généralisons leurs travaux dans le cas de processus de diffusion avec réflexion oblique. Notre résultat requiert la faible convergence des domaines. Notons que cette convergence est plus forte que la convergence dans la topologie de Wijsman, mais plus faible que celle de la topologie de Hausdorff.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 3 (2018), 1408-1431.

Dates
Received: 8 September 2015
Revised: 2 May 2017
Accepted: 4 May 2017
First available in Project Euclid: 11 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1531296024

Digital Object Identifier
doi:10.1214/17-AIHP843

Mathematical Reviews number (MathSciNet)
MR3825886

Zentralblatt MATH identifier
06976080

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J55: Local time and additive functionals 60J65: Brownian motion [See also 58J65] 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Reflected diffusions Oblique reflection Hausdorff convergence Wijsman convergence Weak convergence

Citation

Sarantsev, Andrey. Weak convergence of obliquely reflected diffusions. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), no. 3, 1408--1431. doi:10.1214/17-AIHP843. https://projecteuclid.org/euclid.aihp/1531296024


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