Jumping filtrations and martingales with finite variation

Abstract

On a probability space (ΩℱP), a filtration (ℱ_t)_t≥0 is called a jumping filtration if there is a sequence (T_n) of stopping times increasing to +∞, such that on each set {T_n≤t<T_n+1 the σ-fields ℱ_t and $\mathfrak{F}_{T_n }$ coincide up to null sets. The main result is that (ℱ_t) is a jumping filtration iff all martingales have a.s. locally finite variation.