Fyt sl x fyt x vsy ds fyt x vsy ds

h (fy+h(tl x) - fy(tl x)) = h fy(t - sl x) fy+h(sl y) ds - fy(tl x)) = = h fy(t - sl x) - fy(tl x)) fy+h(sl y) ds - fy(tl x) Jt fy+h(sl y) ds^ —

— (fy(t - sl x) - fy(tl x)) v(s,y) ds - fy(tl x) v(s,y) ds (h — 0) Jo J'

because both the function (fy(t - s| x) - fy(tl x))/s in the first integral, and 1/s in the second integral are continuous and bounded. Corollary is proved.

Let us find the density gt(yl x) of the one-dimensional distribution of I-process, where Px(£(t) G dy) = gt(yl x) dy. We have

9t(y\x) = lim 1 Px(Ty < t, Ty+h > t), h^0 h and also ft

Px(Ty <t,Ty+h > t)= / fy (s\x) fy+h(u\y) duds.

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