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When the state space is $\\mathbb{R}^d$ or the space of positive definite matrices, both types of convergence are obtained under growth conditions on coefficients. These large time convergence results have direct applications in risk-sensitive control and long-term portfolio choice problems.<\/jats:p>","DOI":"10.1137\/13094311x","type":"journal-article","created":{"date-parts":[[2015,1,13]],"date-time":"2015-01-13T11:53:38Z","timestamp":1421150018000},"page":"185-212","source":"Crossref","is-referenced-by-count":9,"title":["Large Time Behavior of Solutions to SemiLinear Equations with Quadratic Growth in the Gradient"],"prefix":"10.1137","volume":"53","author":[{"given":"Scott","family":"Robertson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Xing","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,1,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s002459900067"},{"key":"atypb2","first-page":"127","author":"Bielecki T.","year":"2002","journal-title":"NJ"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s002459900110"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s007800050001"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01259552"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.2009.01533.x"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1080\/14697680701668418"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s11147-008-9018-x"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1080\/14697680701401042"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2010.11.009"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(03)00059-0"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012993258720"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00089"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1026915623"},{"key":"atypb15","unstructured":"A. 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