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Original Articles

Topological Solutions of Noncommutative Stochastic Differential Equations

Pages 961-993 | Received 13 Feb 2006, Accepted 23 Feb 2007, Published online: 30 Aug 2007

REFERENCES

  • Accardi , L. , Fagnola , A. , and Quegebeur , J. 1992 . A representation free quantum stochastic calculus . J. Funct. Anal. 104 : 149 – 197 .
  • Attal , S. , and Lindsay , J.M. 2004 . Quantum stochastic calculus with maximal operator domains . Ann. Prob. 32 : 488 – 529 .
  • Barnett , C. , Streater , R.F. , and Wilde , I.F. 1983 . Quasifree quantum stochastic integrals for the CAR and CCR . J. Funct. Anal. 52 : 19 – 47 .
  • Ekhaguere , G.O.S. 1987 . On noncommutative stochastic integration II . J. Nigerian Math. Soc. 6 : 13 – 32 .
  • Hudson , R. , and Parthasarathy , K.R. 1984 . Quantum Itô's formula and stochastic evolutions . Comm. Math. Physics 93 : 301 – 323 .
  • Parthasarathy , K.R. 1992 . An Introduction to Quantum Stochastic Calculus . Birkhauser Verlag , Bessel .
  • Bichteler , K. 2002 . Stochastic Integration with Jumps . Cambridge University Press , Cambridge .
  • Kloeden , P.E. , and Platen , E. 1992 . The Numerical Solution of Stochastic Differential Equations . Springer-Verlag , Berlin , Heidelberg, New York, London, Paris, Tokyo .
  • Kloeden , P.E. , Platen , E. , and Schurz , H. 1994 . The Numerical Solution of Stochastic Differential Equations through Computer Experiments . Springer-Verlag , Berlin , Heidelberg, New York, London, Paris, Tokyo .
  • Protter , P. 1992 . Stochastic Integration and Differential equations: a new approach . Springer-Verlag , Berlin , Heidelberg, New York, London, Paris, Tokyo, Hong Kong .
  • Revux , D. , and Yor , M. 1991 . Continuous Martingales and Brownian Motion . Springer-Verlag , Berlin , Heidelberg, New York, London, Paris, Tokyo, Hong Kong .
  • Rogers , L.C.G. , and Williams , D. 1987 . Diffusions, Markov Processes, and Martingales, Itô Calculus . Vol. 2 . John Wiley , Chichester , New York, Brisbane, Toronto, Singapore .
  • Stroock , D.W. , Varadhan , S.R.S. 1979 . Multidimensional Diffusion Processes . Springer-Verlag , Berlin , Heidelberg, New York .
  • Ekhaguere , G.O.S. 1992 . Lipschitzian quantum stochastic differential inclusions . Int. J. Theor. Phys. 31 : 2003 – 2027 .
  • Ayoola , E.O. 2002 . Lagrangian quadrature schemes for computing weak solutions of quantum stochastic differential equations . SIAM J. Num. Anal. 39 : 1835 – 1864 .
  • Antoine , J.-P. , Inoue , A. , and Trapani , C. 2002 . Partial *-Algebras and their Operator Realizations . Kluwer Academic Publishers , Dordrecht , Boston, London .
  • Ekhaguere , G.O.S. 1988 . Dirichlet forms on partial *-algebras . Math. Proc. Cambridge Philo. Soc. 104 : 129 – 140 .
  • Ekhaguere , G.O.S. 1991 . Partial W*-dynamical systems . In: Current Topics in Operator Algebras . (eds.), et al. . World Scientific , Singapore , 202 – 217 .
  • Ekhaguere , G.O.S. , and Odiobala , P.O. 1991 . Completely positive conjugate-bilinear maps on partial *-algebras . J. Math. Phy. 32 : 2951 – 2958 .
  • Ekhaguere , G.O.S. 1993. Noncommutative mean ergodic theorem on partial *-algebras. Int. J. Theor. Phy. 32:1187–1196.
  • Ekhaguere , G.O.S. 1996 . Representation of completely positive maps between partial *-algebras . Int. J. Theor. Phy. 35 : 1571 – 1579 .
  • Ekhaguere , G.O.S. 2001 . Algebraic representation of partial algebras . Annales Henri Poincare 2 : 377 – 385 .
  • Itô , K. 1944 . Stochastic integral . Proc. Imper. Acad. Tokyo 20 : 519 – 524 .

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