Remarks on a fractional-time stochastic equation

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Abstract

We consider a class of 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 earlier works. 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.
Original languageEnglish
Number of pages15
JournalProceedings of the American Mathematical Society
Early online date5 Apr 2019
DOIs
Publication statusE-pub ahead of print - 5 Apr 2019

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Stochastic Equations
Fractional
Derivatives
Derivative
Qualitative Behavior
Bounded Domain
Class

Keywords

  • fractional stochastic equation
  • space-time white noise
  • space colored noise

Cite this

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abstract = "We consider a class of 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 earlier works. 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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