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

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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.

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References

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Authors
  1. Yu. B. Koval'
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Additional information

Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 765–768, June, 1994.

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Koval', Y.B. Limiting process for integral functionals of a wiener process on a cylinder. Ukr Math J 46, 832–836 (1994). https://doi.org/10.1007/BF02658185

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  • DOI: https://doi.org/10.1007/BF02658185

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