2020/04/01 by Luca Avena, Avena, Luca, Conrado da Costa +1 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · #60G50 (Primary) 60F15 (Secondary) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2004.00469
openalex publication_date 2020/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The existing criteria for the strong law are either implicit or assume some sufficient decay for the sequence of coefficients. In our set up we allow for arbitrary sequence of coefficients, possibly random, provided the random variables regulated by such increments satisfy some mild concentration conditions. In the non-centered case, convergence can be translated into the behavior of a deterministic sequence and it becomes a game of mass provided the expectation of the random variables is a function of the increments. We show how different limiting scenarios can emerge by identifying several classes of increments, for which concrete examples will be offered.