Abstract: | We prove that integral functionals, whose integrands are bounded functions of a Wiener process on a cylinder, weakly converge
to the processw
1(τ(t)), τ(t) = β1
t + (β2 − β1)mes {s:w
2(s)≥0,s<t}, wherew
1(t andw
2(t) are independent one-dimensional Wiener processes, β1 and β2 are nonrandom values, and β2≥β1≥0.
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 765–768, June, 1994. |