Modified statistical algorithms for filtering and extrapolation in continuous-time stochastic systems

To solve the optimal filtering and extrapolation problems for continuous-time stochastic systems, which are described by stochastic differential equations, we propose new algorithms based on modeling the paths of the special random process with terminating and branching. In previous papers the “maximal section algorithm” has been used, but in this paper we use the definition only for inhomogeneous Poisson flows modeling. Therefore, it is not necessary to build a separate grid for each path of the random process with terminating and branching in the numerical solution of stochastic differential equations. The proposed algorithms are easier, they are preferred for real-time optimal filtering and extrapolation.