{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T09:07:40Z","timestamp":1721812060290},"reference-count":43,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["European Journal of Control"],"published-print":{"date-parts":[[2011,1]]},"DOI":"10.3166\/ejc.17.30-45","type":"journal-article","created":{"date-parts":[[2011,3,11]],"date-time":"2011-03-11T09:40:28Z","timestamp":1299836428000},"page":"30-45","source":"Crossref","is-referenced-by-count":11,"title":["Optimal Control with Random Parameters: A Multiscale Approach"],"prefix":"10.1016","volume":"17","author":[{"given":"Martino","family":"Bardi","sequence":"first","affiliation":[]},{"given":"Annalisa","family":"Cesaroni","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.3166\/ejc.17.30-45_bib0005","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1137\/S0363012900366741","article-title":"Viscosity solutions methods for singular perturbations in deterministic and stochastic control","volume":"40","author":"Alvarez","year":"2001","journal-title":"SIAM J Control Optim"},{"key":"10.3166\/ejc.17.30-45_bib0010","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s00205-003-0266-5","article-title":"Singular perturbations of nonlinear degenerate parabolic PDEs: A general convergence result","volume":"170","author":"Alvarez","year":"2003","journal-title":"Arch Ration Mech Anal"},{"key":"10.3166\/ejc.17.30-45_bib0015","first-page":"1","article-title":"Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations","volume":"204","author":"Alvarez","year":"2010","journal-title":"MemAmer Math Soc"},{"key":"10.3166\/ejc.17.30-45_bib0020","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.jde.2007.05.027","article-title":"Multiscale problems and homogenization for second order Hamilton-Jacobi equations","volume":"243","author":"Alvarez","year":"2007","journal-title":"J Differ Equ"},{"key":"10.3166\/ejc.17.30-45_bib0025","article-title":"Multiscale singular perturbations and homogenization of optimal control problems","volume":"76","author":"Alvarez","year":"2008"},{"key":"10.3166\/ejc.17.30-45_bib0030","series-title":"Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations","author":"Bardi","year":"1997"},{"key":"10.3166\/ejc.17.30-45_bib0035","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1137\/090748147","article-title":"Convergence by viscosity methods in multiscale financial models with stochastic volatility","volume":"1","author":"Bardi","year":"2010","journal-title":"SIAM J Finan Math"},{"key":"10.3166\/ejc.17.30-45_bib0040","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/s000300050027","article-title":"On the Bellman equation for some unbounded control problems","volume":"4","author":"Bardi","year":"1997","journal-title":"NoDEA Nonlinear Differ Equ Appl"},{"key":"10.3166\/ejc.17.30-45_bib0045","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s00526-002-0186-5","article-title":"Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods","volume":"18","author":"Barles","year":"2003","journal-title":"Calc Var Partial Differ Equ"},{"key":"10.3166\/ejc.17.30-45_bib0050","series-title":"Perturbation Methods in Optimal Control","author":"Bensoussan","year":"1988"},{"key":"10.3166\/ejc.17.30-45_bib0055","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1080\/17442508808833511","article-title":"Controlled diffusions in a random medium","volume":"24","author":"Bensoussan","year":"1988","journal-title":"Stochastics"},{"key":"10.3166\/ejc.17.30-45_bib0060","series-title":"Springer Series in Operations Research","article-title":"Perturbation Analysis of Optimization Problems","author":"Bonnans","year":"2000"},{"key":"10.3166\/ejc.17.30-45_bib0065","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s00245-007-0893-6","article-title":"Averaging of singularly perturbed controlled stochastic differential equations","volume":"56","author":"Borkar","year":"2007","journal-title":"Appl Math Optim"},{"key":"10.3166\/ejc.17.30-45_bib0070","doi-asserted-by":"crossref","first-page":"1562","DOI":"10.1137\/060657327","article-title":"Singular perturbations in ergodic control of diffusions","volume":"46","author":"Borkar","year":"2007","journal-title":"SIAM J Control Optim"},{"key":"10.3166\/ejc.17.30-45_bib0075","unstructured":"Bouchard B, Touzi N. Weak Dynamic Programming Principle for Viscosity Solutions. Preprint 2009, available at HAL preprint server"},{"key":"10.3166\/ejc.17.30-45_bib0080","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1002\/cpa.20069","article-title":"Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media","volume":"58","author":"Caffarelli","year":"2005","journal-title":"Comm Pure Appl Math"},{"key":"10.3166\/ejc.17.30-45_bib0085","series-title":"Optimization\u2014Theory and Applications","author":"Cesari","year":"1983"},{"key":"10.3166\/ejc.17.30-45_bib0090","series-title":"Nonsmooth Analysis and Control Theory","author":"Clarke","year":"1998"},{"key":"10.3166\/ejc.17.30-45_bib0095","series-title":"Calcul stochastique et modeles de diffusions","author":"Comets","year":"2006"},{"key":"10.3166\/ejc.17.30-45_bib0100","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-1992-00266-5","article-title":"Users guide to viscosity solutions of second order partial differential equations","volume":"27","author":"Crandall","year":"1992","journal-title":"Bull Amer Math Soc (N. S.)"},{"key":"10.3166\/ejc.17.30-45_bib0105","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1137\/S0363012904440897","article-title":"Uniqueness results for second-order Bellman-Isaacs equations under quadratic growth assumptions and applications","volume":"45","author":"Da Lio","year":"2006","journal-title":"SIAM J Control Optim"},{"key":"10.3166\/ejc.17.30-45_bib0110","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1134\/S0005117906010012","article-title":"Singular perturbations in control problems","volume":"67","author":"Dmitriev","year":"2006","journal-title":"Autom Remote Control"},{"key":"10.3166\/ejc.17.30-45_bib0115","series-title":"Well-Posed Optimization Problems. Lecture Notes in Mathematics, 1543","author":"Dontchev","year":"1993"},{"key":"10.3166\/ejc.17.30-45_bib0120","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1017\/S0308210500018631","article-title":"The perturbed test function method for viscosity solutions of nonlinear PDE","volume":"111","author":"Evans","year":"1989","journal-title":"Proc Roy Soc Edinburgh Sect A"},{"key":"10.3166\/ejc.17.30-45_bib0125","series-title":"Controlled Markov Processes and Viscosity Solutions","author":"Fleming","year":"2006"},{"key":"10.3166\/ejc.17.30-45_bib0130","series-title":"Derivatives in Financial Markets with Stochastic Volatility","author":"Fouque","year":"2000"},{"key":"10.3166\/ejc.17.30-45_bib0135","doi-asserted-by":"crossref","first-page":"1648","DOI":"10.1137\/S0036139902401550","article-title":"Singular perturbations in option pricing","volume":"63","author":"Fouque","year":"2003","journal-title":"SIAM J Appl Math"},{"key":"10.3166\/ejc.17.30-45_bib0140","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1137\/030600291","article-title":"Multiscale stochastic volatility asymptotics","volume":"2","author":"Fouque","year":"2003","journal-title":"Multiscale Model Simul"},{"key":"10.3166\/ejc.17.30-45_bib0145","series-title":"Stochastic Stability of Differential Equations","author":"Hasminskii","year":"1980"},{"key":"10.3166\/ejc.17.30-45_bib0150","series-title":"Mathematical Optimization and Economic Theory","author":"Intriligator","year":"1971"},{"key":"10.3166\/ejc.17.30-45_bib0155","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1512\/iumj.1984.33.33038","article-title":"Uniqueness of unbounded viscosity solution of Hamilton Jacobi equations","volume":"33","author":"Ishii","year":"1984","journal-title":"Indiana Univ Math J"},{"key":"10.3166\/ejc.17.30-45_bib0160","first-page":"129","article-title":"Some asymptotic problems in fully nonlinear elliptic equations and stochastic control","volume":"11","author":"Jensen","year":"1984","journal-title":"Ann Scuola Norm Sup Pisa Cl Sci"},{"key":"10.3166\/ejc.17.30-45_bib0165","series-title":"Differential Games in Marketing","author":"Jorgensen","year":"2004"},{"key":"10.3166\/ejc.17.30-45_bib0170","series-title":"Two-Scale Stochastic Systems. Asymptotic Analysis and Control","author":"Kabanov","year":"2003"},{"key":"10.3166\/ejc.17.30-45_bib0175","series-title":"Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems","author":"Kushner","year":"1990"},{"key":"10.3166\/ejc.17.30-45_bib0180","unstructured":"Lions P-L, Musiela M. Ergodicity of Diffusion Processes, preprint 2002"},{"key":"10.3166\/ejc.17.30-45_bib0185","unstructured":"Lions P-L, Papanicolaou G, Varadhan SRS.Homogenization of Hamilton-Jacobi Equations. Unpublished, 1986"},{"key":"10.3166\/ejc.17.30-45_bib0190","first-page":"233","article-title":"Singular perturbations and time scales in control theory and applications: An overview","volume":"9","author":"Naidu","year":"2002","journal-title":"Dyn Contin Discrete Impuls Syst Ser B Appl Algorithms"},{"key":"10.3166\/ejc.17.30-45_bib0195","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1214\/aop\/1015345596","article-title":"On the Poisson equation and diffusion approximation","volume":"29","author":"Pardoux","year":"2001","journal-title":"I. Ann Probab"},{"key":"10.3166\/ejc.17.30-45_bib0200","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1214\/aop\/1055425774","article-title":"On the Poisson equation and diffusion approximation","volume":"31","author":"Pardoux","year":"2003","journal-title":"II. Ann Probab"},{"key":"10.3166\/ejc.17.30-45_bib0205","series-title":"Optimal Control Theory Applications to Management Science and Economics","author":"Sethi","year":"2000"},{"key":"10.3166\/ejc.17.30-45_bib0210","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1137\/S0363012903409253","article-title":"Bounds and asymptotic approximations for utility prices when volatility is random","volume":"43","author":"Sircar","year":"2004","journal-title":"SIAM J Control Optim"},{"key":"10.3166\/ejc.17.30-45_bib0215","series-title":"Optimal control","author":"Vinter","year":"2000"}],"container-title":["European Journal of Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0947358011705672?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0947358011705672?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T21:23:13Z","timestamp":1543872193000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0947358011705672"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["S0947358011705672"],"URL":"https:\/\/doi.org\/10.3166\/ejc.17.30-45","relation":{},"ISSN":["0947-3580"],"issn-type":[{"value":"0947-3580","type":"print"}],"subject":[],"published":{"date-parts":[[2011,1]]}}}