A deterministic discretisation-step upper bound for state estimation via Clark transformations (Q1773289)

The stability and positivity properties of several discretization schemes for continuous-time state estimation filters are discussed. The authors show that, for robust filters via Clark transformation, one can ensure nonnegative estimated probabilities by choosing a maximum grid step to be no greater than a given bound. It may be noted that standard approximation schemes such as forward Euler or Milstein ones do not preserve positivity. Two types of observation models are studied: the Brownian motion and Poisson process observation models.