On the Dependence of Structure of Multivariate Processes and Corresponding Hitting Times

A direct approach to derive dependence properties among the hitting times of two processes has been initiated by N. Ebrahimi (1987, J. Appl. Probab. 24 115-122) and explored further by N. Ebrahimi and T. Ramalingam (1988, J. Appl. Probab. 25 355-362; 1989, J. Appl Probab. 26 287-295). In this paper new results are obtained for multivariate processes, which help us to identify positive and negative dependent structure among hitting times of the processes. Furthermore, an approach to derive dependence properties among the processes is proposed and a partial solution to the question that what kinds of dependence properties, when they are imposed on processes, are reflected as analogous properties of corresponding hitting times is given.