ANALYSIS OF THE STATISTICAL ERRORS IN CONDITIONED REAL-TIME PATH-INTEGRAL METHODS

An analysis is provided of the statistical errors in the Monte Carlo e valuation of the conditioned real time discretized path integral propa gator, The analysis considers the case of a harmonic potential. For th is case, all the required integrals can be performed analytically. Thi s analysis is also relevant to a semiclassical evaluation of the integ rals in more general problems. It is found (in the simplest case) that the optimal relative statistical error per independent sampling is pr oportional to D(D/2), where D is the dimensionality of the integrand. Therefore, the number of Monte Carlo samplings must scale as D(D) in o rder to achieve a desired level of accuracy. Since D is proportional t o the number of time steps in the discretized path integral, this anal ysis demonstrates that the length of the calculations required increas es very rapidly as the number of time steps is increased.