2012/10/08 by Francesco Caravenna, Caravenna, Francesco · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #26A42 #44A35 #60K05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.CA #math.PR #msc:26A42 #msc:44A35 #msc:60K05
paper · pdf · doi:10.48550/arxiv.1210.2361
14 pages
arxiv created 2012/10/08 · openalex publication_date 2012/10/08 · arxiv updated 2012/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
A non-negative function f, defined on the real line or on a half-line, is said to be directly Riemann integrable (d.R.i.) if the upper and lower Riemann sums of f over the whole (unbounded) domain converge to the same finite limit, as the mesh of the partition vanishes. In this note we show that, for a Lebesgue-integrable function f, very mild conditions are enough to ensure that some n-fold convolution of f with itself is d.R.i.. Applications to renewal theory and to local limit theorems are discussed.