2019
Том 71
№ 11

Limiting process for integral functionals of a wiener process on a cylinder

Koval Yu. B.

Abstract

We prove that integral functionals, whose integrands are bounded functions of a Wiener process on a cylinder, weakly converge to the process $w_1(τ(t)),\, τ(t) = β_1 t + (β_2 − β_1) \text{mes} \{s:w 2(s) ≥ 0,\, s < t\}$, where $w_1(t)$ and $w_2(t)$ are independent one-dimensional Wiener processes, $β_1$ and $β_2$ are nonrandom values, and $β_2 ≥ β_1 ≥ 0$.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 6, pp 832-836.

Citation Example: Koval Yu. B. Limiting process for integral functionals of a wiener process on a cylinder // Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 765–768.

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