Filinkov, A.Elliott, R.J.2025-12-182025-12-182019Stochastic Analysis and Applications, 2019; 37(4):509-5210736-29941532-9356https://hdl.handle.net/11541.2/136534We introduce the notion of a non-linear expectation in spaces of Colombeau generalized functions and provide its characterization in terms of the upper expectation over a set of probability measures. We then study a fully non-linear backward stochastic differential equation in the Colombeau setting via its connection with the corresponding fully non-linear partial differential equation.enCopyright 2019 Taylor & Francis Access Condition Notes: Accepted manuscript available after 1 April 2020generalized solutionsColombeau algebrasnon-linear heat equationG-expectationbackward stochastic differential equationsJournal article10.1080/07362994.2019.15852652-s2.0-85062996547