A stopped Doob inequality for stochastic convolution integrals and stochastic evolution equations

References

• Araujo , A. and Giné , E. 1980 . The centrallimit theorem for real and Banach valued random variables , New York : John Wiley & Sons .
   Google Scholar
• Arnold L. Curtain R.F. Kotelenez P. Nonlinear evolution equations in Hilbert space Forschungsschwerpunkt Dynamische Systeme Universität Bremen Report Nr. 17 1980
   Google Scholar
• Banks , H.T. and Burns , J.A. 1978 . Hereditary control problems: numerical methods based on averaging approximations . SIAM J. Control and Optimization , 16 ( 2 ) : 169 – 208 .
   Web of Science ®Google Scholar
• Billingsley , P. 1968 . Convergence of probability measures , New York : John Wiley .
   Google Scholar
• Chernoff , P.R. 1976 . Two counterexamples i n semigroup theory on Hilbert space . Proc. Amer. Math. Soc , 56 : 253 – 255 .
   Web of Science ®Google Scholar
• Chojnowska-Michalik A. Stochastic differential equations in Hilbert spaces and their applications W.D. Thesis Institute of Mathematics Polish Academy of Science 1976
   Google Scholar
• Curtain , R.F. and Pritchard , A.J. 1978 . Infinite diaensional linear system theory LN incontrol and information sciences , Vol. 8 , Berlin : Springer-Verlag . Heidelberg-New York
   Google Scholar
• Da Prato , G. 1982 . Regularity results of a convolution stochastic integral and applications to parabolic stochastic equations in Hilbert space Pisa Report SCUOLA NORNALE SUPERIORE
   Google Scholar
• Da Prato , G. 1983 . Some results on linear stochastic evolutions equations i n Hilbert space by the semi-groups method . Stoch. Analysis and Applications , 1 ( 1 ) : 57 – 88 .
   Web of Science ®Google Scholar
• Da Prato , G. , Iannelli , M. and Tubaro , L. 1982 . Some results on Liner stochastic differential equations in Hilbert spaces . Stochastics , 6 ( 2 ) : 105 – 116 .
   Google Scholar
• Da Prato , G. , Iannelli , M. and Tubaro , L. 1982 . On the path of regularity of a stochastic process in a Hilbert space defined by the Ito integrals . Stochastics , 6 ( 2 ) : 315 – 322 .
   Google Scholar
• Ichikawa , A. 1982 . Stability of semilinear stochastic evolutions . J. Math. Anal. and Appl , 90 ( 2 ) : 12 – 44 .
   Web of Science ®Google Scholar
• Jacod , J. 1979 . Calcul Stochastique et Problémes de Martingales , Berlin, New York : Springer-Verlag . LN in Mathematics 714
   Google Scholar
• Kato , T. 1976 . “ Perturbation theory for linear operators ” . In Die Grundlehren der math. Wissenschaften , Vol. 132 , Berlin, New York : Springer-Verlag .
   Google Scholar
• Kotelenez , P. 1982 . A submartingale type inequality with applications to stochastic evolution equations . Stochastics , 8 : 139 – 151 .
   Google Scholar
• Kotelenez P. Continuity properties of Hilbert space valued martingales to appear in Stochastic Processes & Applications
   Google Scholar
• Kotelenez , P. 1982 . Law of large numbers and central limit theorem for chemical reactions with diffusion , Bremen . Ph.D. thesis
   Google Scholar
• Kotelenez P. On the caLculus of stochastic evolution equations in Hilbert space - a semigroup approach In preparation
   Google Scholar
• Kotelenez , P. and Curtain , R.F. 1982 . Local behaviour of Hilbert space valued stochastic integrals and the continuity of mild solutions of stochastic evolution equations . Stochastics , 6 : 239 – 257 .
   Google Scholar
• Kurtz , T. 1981 . Approximation of Population Processes, CBMS-NSF Regional Conference Series in Applied Mathematics . SIAM , 36
   Google Scholar
• Metivier , M. 1982 . Semimartingales, Walter de Gruyter Berlin, New York
   Google Scholar
• Metivier , M. and Pellaumail , J. 1980 . On a stopped Doob's inequality and general stochastic equations . Ann, Prob , 8 ( 1 ) : 96 – 114 .
   Web of Science ®Google Scholar
• Metivier , M. and Pellaurnail , J. 1980 . Stochastic Integration , New York : Academic Press .
   Google Scholar
• Pardoux E. Equations aux derivees partielles stochastiquss non linéaires monotones Etude de solutions fortes de type Itô These doct. Sci. inath. Univ. Paris Sud 1975
   Google Scholar
• Tanabe , H. 1979 . Equations of Evolution , Melbourne, , London : Pitman .
   Google Scholar
• Viot , M. 1976 . “ Solution faibles d’équations aux derivées partielles stochastique non Linéaires These doct ” . In Sci. math , Vol. VI , Univ. Paris .
   Google Scholar