Uniform convergence in extended probability of sub-gradients of convex functions

C-Tier
Journal: Economics Letters
Year: 2020
Volume: 188
Issue: C

Score contribution per author:

1.005 = (α=2.01 / 1 authors) × 0.5x C-tier

α: calibrated so average coauthorship-adjusted count equals average raw count

Abstract

It is well known that if a sequence of stochastic convex functions on Rd converges in probability point-wise to some non-stochastic function then the limit function is convex and the convergence is uniform on compact sets; see Andersen and Gill (1982) and Pollard (1991). In the present paper, I establish that if the limiting function is differentiable then any sequence of measurable sub-gradients of the stochastic convex functions converges in extended probability to the gradient of the limit function uniformly on compact sets.

Technical Details

RePEc Handle
repec:eee:ecolet:v:188:y:2020:i:c:s0165176519304100
Journal Field
General
Author Count
1
Added to Database
2026-01-25