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Original Articles

Equations of convolution type with monotone coefficients

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Pages 555-566 | Received 17 Sep 2008, Accepted 01 Jul 2009, Published online: 31 Dec 2009

References

  • Baxendale , P.H. 2005 . Renewal theory and computable convergence rates for geometrically ergodic Markov chains . Ann. Appl. Probab. , 15 ( 1B ) : 700 – 738 .
  • Berenhaut , K.S. and Lund , R.B. 2001 . Geometric renewal convergence rates from hazard rates . J. Appl. Probab. , 38 ( 1 ) : 180 – 194 .
  • Berenhaut , K.S. and Lund , R.B. 2002 . Renewal convergence rates for DHR and NWU lifetimes . Probab. Eng. Inf. Sci. , 16 ( 1 ) : 67 – 84 .
  • Berenhaut , K.S. , Morton , D.C. and Fletcher , P.T. 2005 . Bounds for inverses of triangular Toeplitz matrices . SIAM J. Matrix Anal. Appl. , 27 ( 1 ) : 212 – 217 .
  • Berenhaut , K.S. , Allen , E.E. and Fraser , S.J. 2006 . Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients . Discrete Dyn. Nat. Soc. , Art. ID 40270, 18 pp
  • Berenhaut , K.S. , Guy , R.T. and Vish , N.G. 2008 . A 1-norm bound for inverses of triangular matrices with monotone entries . Banach J. Math. Anal. , 2 ( 1 ) : 112 – 121 .
  • Chung , K.L. and Wolfowitz , J. 1952 . On a limit theorem in renewal theory . Ann. Math. , 2 ( 55 ) : 1 – 6 .
  • Elaydi , S. 1993 . “ Stability of Volterra difference equations of convolution type ” . In Dynamical Systems , Nankai Ser. Pure Appl. Math. Theoret. Phys., 4 66 – 72 . River Edge, NJ : World Scientific Publisher .
  • Elaydi , S. 2005 . An Introduction to Difference Equations , 3rd ed. , New York, NY : Springer .
  • Elaydi , S. , Messina , E. and Vecchio , A. 2007 . On the asymptotic stability of linear Volterra difference equations of convolution type . J. Differ. Equ. Appl. , 13 ( 12 ) : 1079 – 1084 .
  • Erdös , P. , Feller , W. and Pollard , H. 1949 . A property of power series with positive coefficients . Bull. Am. Math. Soc. , 55 : 201 – 204 .
  • Feller , W. 1968 . An Introduction to Probability Theory and its Applications , 3rd ed. , Vol. I , New York-London-Sydney : John Wiley & Sons, Inc. .
  • Heathcote , C.R. 1967 . Complete exponential convergence and some related topics . J. Appl. Probab. , 4 : 217 – 256 .
  • Kendall , D.G. 1959 . “ Unitary dilations of Markov transition operators, and the corresponding integral representations for transition-probability matrices ” . In Probability and Statistics: The Harald Cramér Volume , Edited by: Grenander , Ulf . 139 – 161 . New York, NY : John Wiley & Sons .
  • Kijima , M. 1997 . Markov Processes for Stochastic Modeling , London : Chapman and Hall .
  • Meyn , S.P. and Tweedie , R.L. 1993 . Markov Chains and Stochastic Stability , Communications and Control Engineering Series London : Springer-Verlag London, Ltd .
  • Roberts , G.O. and Polson , N.G. 1994 . On the geometric convergence of the Gibbs sampler . J. R. Stat. Soc. Ser. B , 56 ( 2 ) : 377 – 384 .
  • Rosenthal , J.S. 1995 . Convergence rates for Markov chains . SIAM Rev. , 37 ( 3 ) : 387 – 405 .
  • Vecchio , A. 2003 . A bound for the inverse of a lower triangular Toeplitz matrix . SIAM J. Matrix Anal. Appl. , 24 ( 4 ) : 1167 – 1174 .
  • Vecchio , A. and Mallik , R.K. 2007 . Bounds on the inverses of nonnegative lower triangular Toeplitz matrices wih monoonicity properties . Linear Mulilinear Algebra , 55 ( 4 ) : 365 – 379 .

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