On the Existence and Uniqueness of Solution of Impulsive Quantum Stochastic Differential Equation
Автор(ы):
M. O. Ogundiran
Department of Mathematics
Obafemi Awolowo University,
Ile-Ife. Nigeria.
mogundiran@oauife.edu.ng
V. F. Payne
University of Ibadan,
Ibadan. Nigeria
vpayne34@gmail.com
Аннотация:
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.
Ссылки:
- 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
- E. O. Ayoola, Exponential formula for the reachable sets of quantum stochastic differential inclusions. Stoch. Anal. Appl. 21(2003)3, 515-543
- E. O. Ayoola, Continuous selections of solution sets of Lipschitzian quantum stochastic differential inclusions. Int. J. Theor. Phys. 43(2004) 10, 2041-2059
- E. O. Ayoola, Topological properties of solution sets of Lipschitzian quantum stochastic differential inclusions. Acta Appl. Math. 100 (2008), 15-37
- 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
- M. Benchohra, J. Henderson, S. K. Ntouyas, Impulsive differential equations and inclusions, Hindawi Publishing Corporation, vol 2., New York, (2006)
- K. Deimling, Multivalued differential equations, Walter de Gruyter (1992)
- G. O. S. Ekhaguere, Lipschitzian quantum stochastic differential inclusions. Int. J. Theor. Phys. 31(1992) 11, 2003-2034
- G. O. S. Ekhaguere, Topological solutions of Non commutative stochastic differential equations Stoch. Anal. and Appl. 25(2007) 9, 961-993
- A. Guichardet, Symmetric Hilbert spaces and related topics, Lecture Notes in Mathematics, 261, Springer-Verlag, Berlin(1972)
- E. Hernandez and D. O'Regan: On a new class of Abstract Impulsive differential equations; Proc. Amer. Math. Soc. 141, 5, (2013), 1641-1649
- R. L. Hudson and K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys. 93, (1984)3, 301-323
- K. R. Parthasarathy, An introduction to Quantum stochastic calculus, Monographs in Mathematics 85, Birkhauser Verlag, Basel(1992)
- M. Reed and B. Simon, Methods of Modern Mathematical Physics I. Functional Analysis, 2nd edn., Academic press, New York (1980)
