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Original Articles

Stochastic control and principal eigenvaluetFootnote

Pages 191-211 | Accepted 18 Aug 1983, Published online: 22 Dec 2010

References

  • Donsker , M. D. and Varadhan , S.R.S. 1975 . On the variational formula for the principal eigenvalue for operators with maximum principle . Pro. Nat. Acad. Sci , 72 ( 3 ) : 780 – 783 .
  • Ethier , S. N. and Kurtz , T.G. Markov Processes Existence and Approximation (to appear)
  • Fleming , W. H. 1982 . “ Logarithmic transformations and stochastic control, Advance in Filtering and Optimal Stochastic Control ” . In Springer Lecture Notes in Control and Information Science Edited by: Fleming , W.H. and Gorostiza , L.G. 131 – 141 .
  • Holland , C. J. 1977 . A new energy characterization of the smallest eigenvalue of the Schrodinger equation . Communications on Pure and Appl. Math , 30 : 755 – 765 .
  • Holland , C. J. 1978 . A minimum principle for principal eigenvalue for second order linear elliptic equations with natural boundary conditions . Communications on Pure and Appl Math , 31 : 509 – 519 .
  • Kac , M. 1951 . “ On some connections between probability theory and differential and integral equations ” . In 2nd Berkeley Symposium on Mathematical Statistics and Probability Edited by: Neyman , J. 189 – 215 .
  • Karatzas , I. 1980 . On a stochastic representation for the principal eigenvalue of a second-order differential equation . Stochastics , 3 : 305 – 321 .
  • Krasnosepskii , M. A. 1964 . Positive solutions of operator equations , P Noordhoff LTD .
  • Potter , M. H. and Weinberger , H.F. 1966 . On the spectrum of general second order operators . Bulletin ofAMS ,
  • Sheu , S. J. 1966 . Stochastic control and exit probabilities of jump processes . to appear in SI AM J. on Control and Optimization ,
  • Sheu , S. J. 1982 . Department of Mathematics , Brown University .
  • Sion , M. 1951 . On general minimax theorem . Pacific Math. Journal ,
  • Yosida , K. 1963 . Functional Analysis ,

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