Dynamic reconstruction of disturbances in a quasilinear stochastic differential equation

The problem of reconstructing unknown inputs in a first-order quasilinear stochastic differential equation is studied by applying dynamic inversion theory. The disturbances in the deterministic and stochastic terms of the equation are simultaneously reconstructed using discrete information on some realizations of the stochastic process. The problem is reduced to an inverse one for ordinary differential equations satisfied by the expectation and variance of the original process. A finite-step software implementable solution algorithm is proposed, and its accuracy with respect to the number of measured realizations is estimated. An illustrative example is given.