On the relation between Rossi alpha and Feynman alpha methods

The present paper revisits the issue. We examine the multi mode formulae obtained by Munoz Cobo et al. in order to assess the validity of the above relationship. We show that indeed it is possible to derive the Feynman alpha formula by a double integration of the Rossi alpha formula followed by some elementary algebraic manipulation. To demonstrate the generality of this relationship we use two distinct approaches. In the first of these, we show, using the (backward) stochastic transport equation and the space dependent Bartlett formula, that the Rossi alpha and Feynman alpha functions obey the above relationship. In the second, we start from the theory of stochastic point processes and show that the relationship is quite general.