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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 81, 2009 - Issue 3-4: Stochastic Analysis
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Original Articles

Pascal white noise calculus

, &
Pages 323-343 | Received 18 May 2008, Accepted 08 Feb 2009, Published online: 23 Jul 2009

References

  • Accardi , L. and Boukas , A. 2006 . The emergence of the Virasoro and w∞-algebras throught the renormalized powers of quantum white noise . Inst. J. Math. Comput. Sci. , 1 ( 3 ) : 315 – 341 .
  • Accardi , L. and Boukas , A. 2006 . Renormalized higher powers of white noise (RHPWN) and conformal field theory . Infin. Dimens. Anal. Quantum Probab. Relat. Top. , 9 ( 3 ) : 379 – 390 .
  • Accardi , L. , Boukas , A. and Franz , U. 2006 . Renormalized powers of quantum white noise . Infin. Dimens. Anal. Quantum Probab. Relat. Top. , 9 ( 1 ) : 129 – 147 .
  • Albeverio , S. , Daletsky , Yu.L. , Kondratiev , Yu.G. and Streit , L. 1996 . Non-Gaussian infinite dimensional analysis . J. Funct. Anal. , 138 : 311 – 350 .
  • Asai , N. , Kubo , I. and Kuo , H.-H. 2004 . Multiplicative renormalization and generating functions II . Taiwan. J. Math. , 8 ( 4 ) : 583 – 628 .
  • Barhoumi , A. , Ouerdiane , H. and Riahi , A. On spectral approach to pascal white noise functional . Stoch. Anal. Appl. , (to appear)
  • Ben Chrouda , M. , Eloued , M. and Ouerdiane , H. 2002 . Convolution calculus and applications to stochastic differential equation . Soochow J. Math. , 28 ( 4 ) : 375 – 388 .
  • Berezansky , Y.M. and Mierzejewski , D.A. 2003 . The construction of the chaotic representation for the gamma field . Infin. Dimens. Anal. Quantum Probab. Relat. Top. , 6 ( 1 ) : 33 – 56 .
  • Bourbaki , N. 1950 . Functions D'une Variable Réelle. Eléments de Mathématiques, Livre IV , Paris : Hermann et Cie .
  • Chaari , S. and Ouerdiane , H. 2007 . White noise analysis in the Poisson space . Afr. Diaspora J. Math. , 4 ( 2 ) : 103 – 119 .
  • Chihara , T.S. 1978 . An Introduction to Orthogonal Polynomials , New York : Gordon and Breach .
  • Denis , L. 2000 . A criterion of density for solutions of Poisson-driven SDEs . Probab. Theory Relat. Fields , 118 : 406 – 426 .
  • Di Nunno , G. , Øksendal , B. and Proske , F. 2004 . White noise analysis for Lévy processes . J. Funct. Anal. , 206 ( 1 ) : 109 – 148 .
  • Gannoun , R. , Hchaichi , R. , Ouerdiane , H. and Rezgui , A. 2000 . Un théorème de dualité entre espaces de fonctions holomorphes à croissance exponentielle . J. Funct. Anal. , 171 ( 1 ) : 1 – 14 .
  • Gradstein , I. and Ryshik , I. 1981 . Tables of Series, Products and Integrals , Vol. 1 , Frankfurt. M : Verlag Harri Deutsch Thun .
  • Hida , T. 1975 . Analysis of Brownian Functionals , Carleton Mathematical Lecture Notes Vol. 13 ,
  • Hida , T. , Kuo , H.-H. , Potthoff , J. and Streit , L. 1993 . White Noise: An Infinite dimensional Calculus , Dordrecht, Boston, London : Kluwer Academic Publishers .
  • Itô , Y. 1988 . Generalized Poisson functionals . Probab. Theory Relat. Fields , 77 : 1 – 28 .
  • R. Koekoek and R.F. Swarttouw, The askey-sheme of hypergeometric orthogonal polynomials and its q-analogue, Delft University of Technology, Report No. 98-17 (1998)
  • Kondratiev , Yu.G. , Leukert , P. , Streit , L. and Yan , J.A. 1996 . Wick calculus in Gaussian analysis . Acta Appl. Math. , 44 : 269 – 294 .
  • Kuo , H.-H. 1996 . White Noise Distrubition Theory , Boca Raton : CRC Press .
  • Lee , Y.-J. and Shih , H.-H. 1999 . The Segal–Bargmann transform for Lévy functionals . J. Funct. Anal. , 168 : 46 – 83 .
  • Lyvynov , E.W. , Rebenko , A.L. and Shchepan'uk , G.V. 1997 . Wick calculus on spaces of generalized functions of compound Poisson white noise . Rep. Math. Phys. , 23 ( 2 ) : 219 – 248 .
  • Obata , N. 1994 . “ White noise calculus and Fock space ” . In Lecture Notes in Mathematics , Vol. 1577 , New York, NY : Springer-Verlag .
  • Obata , N. 1999 . Wick product of white noise operators and quantum stochastic differential equation . J. Math. Soc. Jpn , 51 : 613 – 641 .
  • J.L. Silva, Studies in non-Gaussian analysis, Ph.D. Dissertation, University of Maderira, 1998

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