Some general strong laws for weighted sums of stochastically dominated random variables

For weighted sums, general strong laws of large numbers of the form almost certainly are established where the random variables are stochastically dominated by a random variable are suitable conditional expectations or are all 0. The hypotheses involve both the behavior of the tail of the distribution of ∣Y∣ and the growth behavior of the constants bn/an. In general, no assumptions are made regarding the joint distributions of . As special cases, both old and new results are obtained