Fundamental Theorem of Calculus for Backwards Ito Integral
In this paper, a definition of backwards stochastic differentiation is introduced. A necessary and sufficient set of conditions for backwards Ito integration and differentiation to be reversible processes is given. Backwards Ito integration is defined using the generalized Riemann approach.
Arcede, J.P., Cabral, E.A. (2013). Fundamental Theorem of Calculus for the Backwards Ito Integral. Matimyas Matematika, 34(1-2), 1-9.