Remarks on a fractional-time stochastic equation

Foondun, Mohammud

doi:10.1090/proc/14644

Remarks on a fractional-time stochastic equation
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Proc. Amer. Math. Soc. 149 (2021), 2235-2247 Request permission

Abstract:

We consider a class of a fractional-time stochastic equation defined on a bounded domain and show that the presence of the time derivative induces a significant change in the qualitative behaviour of the solutions. This is in sharp contrast with the phenomenon showcased in [ALEA Lat. Am. J. Probab. Math. Stat. 12 (2015), pp. 551–571] and extented in [Stochastic Process Appl. 126 (2016), pp. 1184–1205] and [Electron. Commun. Probab. 23 (2018)]. We also show that as one tunes off the fractional in the fractional time derivative, the solution behaves more and more like its usual counterpart.

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