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On the Existence and Uniqueness of Solution of Impulsive Quantum Stochastic Differential Equation


M. O. Ogundiran

Department of Mathematics
Obafemi Awolowo University,
Ile-Ife. Nigeria.

V. F. Payne

University of Ibadan,
Ibadan. Nigeria


This paper is concerned with the existence and uniqueness of solutions of quantum stochastic differential equations (QSDE) subject to certain impulse effects. The QSDE in our work is within the framework of the Hudson-Parthasarathy formulation of quantum stochastic calculus.


  1. R. P. Agarwal and D. O'Regan, Multiple nonnegative solutions for second order impulsive differential equations, Applied Mathematics and Computation 114 (2000), 1, 51-59
  2. E. O. Ayoola, Exponential formula for the reachable sets of quantum stochastic differential inclusions. Stoch. Anal. Appl. 21(2003)3, 515-543
  3. E. O. Ayoola, Continuous selections of solution sets of Lipschitzian quantum stochastic differential inclusions. Int. J. Theor. Phys. 43(2004) 10, 2041-2059
  4. E. O. Ayoola, Topological properties of solution sets of Lipschitzian quantum stochastic differential inclusions. Acta Appl. Math. 100 (2008), 15-37
  5. E. O. Ayoola and A. W. Gbolagade, Further results on the existence, uniqueness and stability of strong solutions to quantum stochastic differential equations. Applied Mathematics Letters 18, (2005) 219-227
  6. M. Benchohra, J. Henderson, S. K. Ntouyas, Impulsive differential equations and inclusions, Hindawi Publishing Corporation, vol 2., New York, (2006)
  7. K. Deimling, Multivalued differential equations, Walter de Gruyter (1992)
  8. G. O. S. Ekhaguere, Lipschitzian quantum stochastic differential inclusions. Int. J. Theor. Phys. 31(1992) 11, 2003-2034
  9. G. O. S. Ekhaguere, Topological solutions of Non commutative stochastic differential equations Stoch. Anal. and Appl. 25(2007) 9, 961-993
  10. A. Guichardet, Symmetric Hilbert spaces and related topics, Lecture Notes in Mathematics, 261, Springer-Verlag, Berlin(1972)
  11. E. Hernandez and D. O'Regan: On a new class of Abstract Impulsive differential equations; Proc. Amer. Math. Soc. 141, 5, (2013), 1641-1649
  12. R. L. Hudson and K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys. 93, (1984)3, 301-323
  13. K. R. Parthasarathy, An introduction to Quantum stochastic calculus, Monographs in Mathematics 85, Birkhauser Verlag, Basel(1992)
  14. M. Reed and B. Simon, Methods of Modern Mathematical Physics I. Functional Analysis, 2nd edn., Academic press, New York (1980)

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