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Subordinated stochastic processes with aged operational time.

V P Shkilev1

  • 1Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, 17, General Naumov Str., 03164 Kiev, Ukraine.

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Summary

This study analyzes subordinated stochastic processes using renewal processes as operational time. We derived formulas for probability density functions and calculated correlation functions for aged processes, modeling relaxation in disordered media.

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Area of Science:

  • Stochastic processes
  • Probability theory
  • Statistical physics

Background:

  • Subordinated stochastic processes are crucial for modeling complex systems.
  • Renewal processes are fundamental to understanding operational time in systems.
  • Understanding aged processes requires advanced analytical techniques.

Purpose of the Study:

  • To analyze subordinated stochastic processes with renewal processes as operational time.
  • To derive a recurrence formula for multipoint probability density functions of aged renewal processes.
  • To model relaxation phenomena in disordered media.

Main Methods:

  • Derivation of a recurrence formula for probability density functions.
  • Calculation of two-point correlation functions.
  • Development of a relaxation model for disordered media.

Main Results:

  • A recurrence formula for multipoint probability density functions of aged renewal processes was successfully derived.
  • Two-point correlation functions were calculated for specific subordinated processes, including the generalized Ornstein-Uhlenbeck process.
  • A novel model for relaxation in disordered media with traps and obstacles was proposed.

Conclusions:

  • The derived formulas provide a powerful tool for analyzing aged renewal processes.
  • The calculations offer insights into the behavior of subordinated stochastic processes.
  • The proposed model advances the understanding of relaxation dynamics in complex media.