A second order time discretization of the solution of the non-linear   filtering problem
  The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of these functionals corresponding to a chosen partition of the time interval and show that the convergence rate of discretisation is proportional with the square of the mesh of the partition. 
Dan Crisan and Salvador Ortiz-Latorre
math.PR