Subordinated stochastic processes with aged operational time
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Updated: Feb 14, 2026

The Microfluidic Probe: Operation and Use for Localized Surface Processing
Published on: June 4, 2009
1Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, 17, General Naumov Str., 03164 Kiev, Ukraine.
Abstract:
In this paper, subordinated stochastic processes are considered, where the renewal process acting as the operational time. It is assumed that the observation of the process begins at a certain time after the start of the renewal process. A recurrence formula was derived for calculating the multipoint probability density functions of the aged renewal process. Two-point correlation functions for certain subordinated stochastic processes, particularly for the generalized Ornstein-Uhlenbeck process, were calculated. A model of relaxation in a disordered medium with traps and obstacles is proposed.
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