Linearly Positive Histories: Probabilities for a Robust Family of   Sequences of Quantum Events
  Nonnegative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories. The resulting {\it linearly positive histories} avoid the highly restrictive decoherence conditions and yet give the same probabilities when those conditions apply. Thus linearly positive histories are a broad extension of decohering histories. Moreover, the resulting theory is manifestly time-reversal invariant. 
Sheldon Goldstein (Rutgers University) and Don N. Page (University of   Alberta)