Abstract
Krener and collaborators have shown that Gaussian Reciprocal Diffusions (GRDs) x(t) must satisfy on [0,T] a 2nd order stochastic differential equation of the form , where ξ(t) is a generalized noise process. Krener has also shown that such GRDs have conditional moments satisfying a system of conservation laws similar to those of continuum mechanics In this paper we further investigate the relationship between GRDs. their conditional moments and their associated conservation laws. We show that a GRD is determined by its lifetime, its reciprocal invariants and the initial values of its conditional moments. A characterization is then given of those functions that are allowable as the initial values for the conditional moments of a GRD having a given lifetime and given reciprocal invariants. We show further that the conservation laws associated with a GRD form a hyperbolic system for either all or none of the process lifetime, and we give criteria for determining which of these alternatives holds
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