Lp-Theory for the fractional time stochastic heat equation with an infinite-dimensional fractional Brownian motion
2021 ◽
Vol 24
(02)
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pp. 2150010
Keyword(s):
In this paper, we study the [Formula: see text]-theory of the fractional time stochastic heat equation [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] denotes the Caputo derivative of order [Formula: see text], and [Formula: see text] is a sequence of i.i.d. fractional Brownian motions with a same Hurst index [Formula: see text]. The integral with respect to fractional Brownian motion is the Skorohod integral. By using the Malliavin calculus techniques and fractional calculus, we obtain a generalized Littlewood–Paley inequality, and prove the existence and uniqueness of [Formula: see text]-solution to such equation.
2015 ◽
Vol 3
(2)
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pp. 133-158
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2009 ◽
Vol 14
(0)
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pp. 55-65
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2018 ◽
Vol 70
(1)
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pp. 1-6
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2014 ◽
Vol 51
(1)
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pp. 1-18
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