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Abstract. Let {X ni | 1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively dependent (N D) random variables. We in this paper discuss the conditions of P n i=1 a ni X ni → 0 completely as n → ∞ under not necessarily identically distributed setting and the strong law of large numbers for weighted sums of arrays of rowwise negatively dependent random variables is also considered.

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In this paper we introduce a new concept of θ conditionally independent and positive and negative quadrant dependent on I 1 , I 2 and I 3 for bivariate stochastic processes and their hitting times and we are given some theorems and examples to illustrate these concepts.

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