Kemp, Gordon (2020) 'Uniform Convergence in Extended Probability of Sub-Gradients of Convex Functions.' Economics Letters, 188. p. 108809. ISSN 0165-1765

Preview

Text ucp-final.pdf - Accepted Version Download (246kB) | Preview

Abstract

It is well known that if a sequence of stochastic convex functions on $\mathbb{R}^{d}$ 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.

Item Type:	Article
Uncontrolled Keywords:	Convex functions, sub-gradients, convergence in probability, extended probability measure, uniform convergence
Divisions:	Faculty of Social Sciences Faculty of Social Sciences > Economics, Department of
SWORD Depositor:	Elements
Depositing User:	Elements
Date Deposited:	18 Nov 2019 11:56
Last Modified:	18 Aug 2022 12:20
URI:	http://repository.essex.ac.uk/id/eprint/25893

Actions (login required)

View Item