A review of some recent results on quantum stochastic dierential

equations and inclusions

E. O. Ayoola

Department of Mathematics, University of Ibadan, Ibadan, Nigeria

Abstract. 

Building upon the fundamental foundation laid by Ekhaguere in his pioneering work concerning

the existence and some qualitative properties of Lipschitzian quantum stochastic dierential inclusions

rendered in the framework of the Hudson-Parthasarathy formulation (H-P) of quantum stochastic calculus

(QSC), this paper reviews our important results in this eld. The review covers the period 1992 to the

year 2010 and it concerns both the theoretical and numerical aspects of quantum stochastic dierential

equations (QSDE) and inclusions (QSDI) driven by quantum martingales and semi-martingales in the

weak and strong sense. It is well known that the H-P formulation of QSC suciently generalise the Ito

calculus.

Keywords: quantum stochastic dierential equations, inclusions, martingales, Ito calculus.