# Erratum to: Risk-Sensitive Control with Near Monotone Cost

Erratum to: Risk-Sensitive Control with Near Monotone Cost Appl Math Optim (2010) 62: 165–167 DOI 10.1007/s00245-010-9100-2 ERRATUM Erratum to: Risk-Sensitive Control with Near Monotone Cost Anup Biswas · V.S. Borkar · K. Suresh Kumar Published online: 13 April 2010 © Springer Science+Business Media, LLC 2010 Erratum to: Appl Math Optim DOI 10.1007/s00245-009-9096-7 We have used Theorem 3 of [2] in the proof of Theorem 2.1 in order to claim ρ ≤ β , and also in a remark preceding Theorem 2.2. The proof thereof in [2], however, is ﬂawed. Our own proof of the reverse inequality ρ ≥ β also has gaps. We give an alternative proof of ρ = β below that sidesteps both difﬁculties. Let χ denote a nonnegative smooth function such that χ ≡ 1in B := {x :x≤ n k k k}, χ ≡ 0in B and 0 ≤ χ ≤ 1. Let r = rχ . Deﬁne for α> 0, k k k k k+1 −αt α θ e r (X ,v )dt k t t u (θ , x) := inf E [e ]. v∈M The online version of the original article can be found under doi:10.1007/s00245-009-9096-7. A. Biswas Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore 560065, India 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

, Volume 62 (2) – Oct 1, 2010
3 pages

/lp/springer_journal/erratum-to-risk-sensitive-control-with-near-monotone-cost-ZYsd5rnKEQ
Publisher
Springer-Verlag
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
D.O.I.
10.1007/s00245-010-9100-2
Publisher site
See Article on Publisher Site

### Abstract

Appl Math Optim (2010) 62: 165–167 DOI 10.1007/s00245-010-9100-2 ERRATUM Erratum to: Risk-Sensitive Control with Near Monotone Cost Anup Biswas · V.S. Borkar · K. Suresh Kumar Published online: 13 April 2010 © Springer Science+Business Media, LLC 2010 Erratum to: Appl Math Optim DOI 10.1007/s00245-009-9096-7 We have used Theorem 3 of [2] in the proof of Theorem 2.1 in order to claim ρ ≤ β , and also in a remark preceding Theorem 2.2. The proof thereof in [2], however, is ﬂawed. Our own proof of the reverse inequality ρ ≥ β also has gaps. We give an alternative proof of ρ = β below that sidesteps both difﬁculties. Let χ denote a nonnegative smooth function such that χ ≡ 1in B := {x :x≤ n k k k}, χ ≡ 0in B and 0 ≤ χ ≤ 1. Let r = rχ . Deﬁne for α> 0, k k k k k+1 −αt α θ e r (X ,v )dt k t t u (θ , x) := inf E [e ]. v∈M The online version of the original article can be found under doi:10.1007/s00245-009-9096-7. A. Biswas Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore 560065, India

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2010

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