lR.
O P ,x, y = l' 1m a~l,bir (s(x) - s(a))(s(b) - s(y)) (b) () , s - s a Under the same assumptions but with l reflecting, we have 1/Jo Go(x,y) = lim(s(b) - s(y)), bir x ~ y. x ~ y. == 1 and hence 20 II LINEAR DIFFUSIONS It can be proved (Ito and McKean (1974) p. 149) that (t, x) f---+ p(t; x,·) solves for t > 0 and x E intI the generalized parabolic differential equation a at u(t, x) = gu(t, x). This is the so called backward Kolmogorov equation for X. ) at land r can be deduced from the corresponding conditions for 'ljJa and i{Ja given in No.
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