Before revision:  By focussing on the properties that martingales and compensators show on infinitesimally small intervals, the classical martingale concept is extended and corresponding martingale representations are developed. The extended representations make it possible to generalize Thiele's equation in insurance mathematics to situations where information restrictions apply .
After revision:  By focussing on the properties that martingales and compensators show on infinitesimally short intervals. Infinitesimal martingale representations are derived that extend classical martingale representations to non-monotone information. While the classical representations describe innovations only, the extended representations have an additional symmetric counterpart that quantifies the effect of information loss .