On a Diffusion Process with Non-static Restarts Subjected to a Time-Varying Potential

Authors

DOI:

https://doi.org/10.22481/intermaths.v5i1.14959

Keywords:

Brownian Motion in a Potential, Stochastic Resetting, Auto-Correlation, Quadratic Cost, First-Passage Time

Abstract

We consider a diffusive particle subjected to non-static resettings, i.e. the resetting positions vary with time. The particle is also immersed in a time-dependent potential field which is not affected by the resettings. We exhibit new results concerning the moments and the auto-correlation of the process. We observe that a positive correlation always exists between past and future. Moreover, we discuss the cost that is needed to keep restarting the process until a defined task is performed. Furthermore, we give examples of the process behaviour in various situations by means of either analytical results or computational simulations, verifying an important relation between the potential and the resetting function. In particular, the examples indicate that the existence of the potential field may hinder the accomplishement of a task, even in the presence of resetting.

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Published

2024-06-30

How to Cite

Silva, T. T. da. (2024). On a Diffusion Process with Non-static Restarts Subjected to a Time-Varying Potential. INTERMATHS, 5(1), 26-41. https://doi.org/10.22481/intermaths.v5i1.14959

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Vol. 5 No. 1 (2024)

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Artigos

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