Limiting process for integral functionals of a wiener process on a cylinder - Koval, Yu. B. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
We prove that integral functionals, whose integrands are bounded functions of a Wiener process on a cylinder, weakly converge to the process w_1(τ(t)), τ(t) = β_1 t + (β_2 − β_1) mes {s:w 2(s) ≥ 0, s < t}, where w_1(t) and w_2(t) are independent one-dimensional Wiener processes, β_1 and β_2 are nonrandom values, and β_2 ≥ β_1 ≥ 0.