Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
On the dependence of structure of multivariate processes and corresponding hitting times
Journal of Multivariate Analysis
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A direct approach to derive dependence properties among components of multi-dimensional stochastic processes has been discussed by N. Ebrahimi (1994, J. Multivariate Anal. 50, 55-67). Dependence properties among hitting times involving multi-dimensional stochastic processes has been initiated by N. Ebrahimi (1987, J. Appl. Probab. 24, 115-122) and explored further by N. Ebrahimi and T. Ramalingham (1988, J. Appl. Probab. 25, 355-362; 1989, J. Appl. Probab. 26, 287-295). Let X(t) = (X1(t),..., Xk(t)) be an Ito process assuming values in Rk. In this article, under certain conditions, we show that the process X(t) has a certain dependence structure. We also consider the first passage problem involving X(t) and discuss the dependence structure among hitting times of X1(t),..., and Xk(t).