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Time changed spherical Brownian motions with longitudinal drifts

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  • Ascione, Giacomo
  • Vidotto, Anna

Abstract

We consider a time change of a drifted Brownian motion on the two-dimensional unit sphere. Precisely, we find strong solutions to the related time-nonlocal Kolmogorov equation under suitably regular initial data and we determine the spectral decomposition of its probability density function. Moreover, we study the speed of convergence to the stationary state, proving a non-exponential rate to the equilibrium. Finally, we provide very weak solutions of the same time-nonlocal Kolmogorov equation with general initial data. These results improve the known ones in terms of both the presence of a perturbation and the generality of the initial data.

Suggested Citation

  • Ascione, Giacomo & Vidotto, Anna, 2025. "Time changed spherical Brownian motions with longitudinal drifts," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:spapps:v:181:y:2025:i:c:s0304414924002552
    DOI: 10.1016/j.spa.2024.104547
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    References listed on IDEAS

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    1. Meerschaert, Mark M. & Toaldo, Bruno, 2019. "Relaxation patterns and semi-Markov dynamics," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2850-2879.
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    5. D’Ovidio, Mirko & Leonenko, Nikolai & Orsingher, Enzo, 2016. "Fractional spherical random fields," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 146-156.
    6. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2006. "Stochastic model for ultraslow diffusion," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1215-1235, September.
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