Sensitivity analysis in stochastic mechanics

The formalism of sensitivity analysis for stochastic differential equations is adapted and extended to the framework of stochastic mechanics. Thus a methodology is provided for analyzing the dependence of expectations of functionals of the stochastic mechanical diffusion process on parameters defining the system. This should prove useful in numerical simulations employing the latter theory. We take into account the fact that in stochastic mechanics typically a probability distribution of initial positions (rather than the initial position itself) is prescribed. The expression for a sensitivity density with respect to a drift variation depending only on time is shown to follow from the Ito-Girsanov formula, which is also employed to develop new formulas for sensitivity densities with respect to position-dependent drift variations. As an example to verify these techniques, the sensitivity coefficients of the harmonic-oscillator correlation function with respect to the angular frequency and the diffusion constant are calculated; the results coincide with those obtained by direct differentiation.