We study the properties of strong random operators T t in L 2(ℝ) used to describe the shifts of functions along an Arratia flow. We prove the formula of change of variables for the Arratia flow. As a consequence of this formula, we establish sufficient conditions for compact sets K ⊂ L 2(ℝ) under which T t has a continuous modification on K. We also present necessary and sufficient conditions for the convergent sequences in L 2(ℝ) under which the operator T t preserves their convergence.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 2, pp. 157–172, February, 2017.
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Korenovskaya, Y.A. Properties of Strong Random Operators Generated by the Arratia Flow. Ukr Math J 69, 186–204 (2017). https://doi.org/10.1007/s11253-017-1356-0
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DOI: https://doi.org/10.1007/s11253-017-1356-0