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Erratum to: Risk-Sensitive Control with Near Monotone Cost

Erratum to: Risk-Sensitive Control with Near Monotone Cost Appl Math Optim (2010) 62: 435–438 DOI 10.1007/s00245-010-9119-4 ERRATUM Erratum to: Risk-Sensitive Control with Near Monotone Cost Anup Biswas · V.S. Borkar · K. Suresh Kumar Published online: 25 September 2010 © Springer Science+Business Media, LLC 2010 Erratum to: Appl Math Optim DOI 10.1007/s00245-009-9096-7 In this note we give further corrections to [1] in addition to [2]. Awkwardness of such an exercise notwithstanding, the results come out much stronger than what was originally proposed: a key assumption (A2) can be significantly weakened. In the proof of Theorem 2.1, the argument after (2.14) is not correct. So we give an alternate proof for [1, Theorem 2.1]. Note that u (θ , x) given by (2.5) of [1] satisfies the p.d.e. ∂u 1 α α 2 α α αθ = inf ∇u · b(x, v ) + θr(x, v )u + tr(a(x)∇ u ), u (0,x) = 1. 1 1 ∂θ v ∈V 2 1 1 The online version of the original article can be found under doi:10.1007/s00245-009-9096-7. Research of V.S. Borkar supported in part by a grant from General Motors India Lab. A. Biswas Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore 560065, India e-mail: anup@math.tifrbng.res.in V.S. Borkar http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Erratum to: Risk-Sensitive Control with Near Monotone Cost

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References (4)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-010-9119-4
Publisher site
See Article on Publisher Site

Abstract

Appl Math Optim (2010) 62: 435–438 DOI 10.1007/s00245-010-9119-4 ERRATUM Erratum to: Risk-Sensitive Control with Near Monotone Cost Anup Biswas · V.S. Borkar · K. Suresh Kumar Published online: 25 September 2010 © Springer Science+Business Media, LLC 2010 Erratum to: Appl Math Optim DOI 10.1007/s00245-009-9096-7 In this note we give further corrections to [1] in addition to [2]. Awkwardness of such an exercise notwithstanding, the results come out much stronger than what was originally proposed: a key assumption (A2) can be significantly weakened. In the proof of Theorem 2.1, the argument after (2.14) is not correct. So we give an alternate proof for [1, Theorem 2.1]. Note that u (θ , x) given by (2.5) of [1] satisfies the p.d.e. ∂u 1 α α 2 α α αθ = inf ∇u · b(x, v ) + θr(x, v )u + tr(a(x)∇ u ), u (0,x) = 1. 1 1 ∂θ v ∈V 2 1 1 The online version of the original article can be found under doi:10.1007/s00245-009-9096-7. Research of V.S. Borkar supported in part by a grant from General Motors India Lab. A. Biswas Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore 560065, India e-mail: anup@math.tifrbng.res.in V.S. Borkar

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Dec 1, 2010

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