Result: Asymptotic normality of randomly truncated stochastic algorithms

Title:
Asymptotic normality of randomly truncated stochastic algorithms
Authors:
Lelong, Jérôme
Contributors:
Mathématiques financières (MATHFI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS)
Source:
ESAIM: Probability and Statistics. 17:105-119
Publisher Information:
CCSD; EDP Sciences, 2013.
Publication Year:
2013
Collection:
collection:ENPC
collection:UGA
collection:CNRS
collection:UNIV-GRENOBLE1
collection:UNIV-PMF_GRENOBLE
collection:INPG
collection:INSMI
collection:PARISTECH
collection:LJK
collection:LJK_PS
collection:LJK_PS_MATHFI
collection:UGA-TEST-QUATER
collection:TDS-MACS
collection:TEST-UGA
Subject Terms:
stochastic approximation, randomly truncated stochastic algorithms, central limit theorem, martingale arrays, MSC: 62L20; 60F05; 62F12, [MATH.MATH-PR]Mathematics [math], Probability [math.PR], [MATH.MATH-OC]Mathematics [math], Optimization and Control [math.OC]
Original Identifier:
HAL: hal-00464380
Document Type:
Journal article<br />Journal articles
Language:
English
ISSN:
1292-8100
1262-3318
Relation:
info:eu-repo/semantics/altIdentifier/doi/10.1051/ps/2011110
DOI:
10.1051/ps/2011110
Access URL:
https://hal.science/hal-00464380
https://hal.science/hal-00464380v2/document
https://hal.science/hal-00464380v2/file/truncated_sa_tcl_2.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.hal.00464380v2
Database:
HAL

Further Information

We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly easy to check in practice.