In this paper, we show that despite their distinction, both the Statonovich and Îto s
calculi lead to the same reactive Fokker-Planck equation: ∂p∂t−∂∂x[D∂p∂x−bp]=λmp, (1)
describing stochastic dynamics of a particle moving under the influence of an
indefinite potential m(x,t), a drift b(x,t), and a constant diffusion D. We treat
the periodic-parabolic eigenvalue problem (1) for finite domains having
absorbing barriers. We show that under conditions required by the maximum
principle, the positive principal eigenvalue λ* (and the negative principal λ*
eigenvalue) is connected to the probability eigendensity function p(x,t) by a
Raleigh-Ritz like formulation. In the process, we establish the manner of effect of
the drift and any inducing potential on the size of the principal eigenvalue. We
show that the degree of convexity of the potential plays a major role in this
regard.