  A new application of duality relations of stochastic processes is
demonstrated. Although conventional usages of the duality relations need
analytical solutions for the dual processes, we here employ numerical solutions
of the dual processes and investigate the usefulness. As a demonstration,
estimation problems of hidden variables in stochastic differential equations
are discussed. Employing algebraic probability theory, a little complicated
birth-death process is derived from the stochastic differential equations, and
an estimation method based on the ensemble Kalman filter is proposed. As a
result, the possibility for making faster computational algorithms based on the
duality concepts is shown.
