On some matters concerning the backward and forward equations of probability balance for neutrons in a medium with randomly time-varying properties

The recent contributions to combined zero-power and at-power neutron noise analysis raises a number of interesting questions which deserve further discussion [Kitamura, Y., Pal, L., Pazsit, I., Yamamoto, A., Yamane, Y., Some properties of zero power neutron noise in a time-varying medium with delayed neutrons. Annals of Nuclear Energy, in press.]. It is shown, for example, by direct calculation, that the forward equation of probability balance is exact when combined with a dichotomic Markov process to describe the random physical behaviour of a medium, whereas the backward equation contains errors. This confirms and corroborates the assertions of Pal L. and Pazsit I. [2006. Neuron fluctuations in a multiplying medium randomly varying in time. Physica Scripta 74, 62.] who first pointed out this anomaly. Extensions to spatially random media are discussed, together with an application to the calculation of the extinction probability. Other methods of solution such as that of polynomial chaos are briefly touched upon. In order to carry out the calculations described we use the stochastic ansatz concept [Williams, M.M.R., 2008a. A stochastic ansatz and its relationship with the dichotomic Markov process. Physica A 387, 4997.].