ON LP -SOLUTION OF FRACTIONAL HEAT EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION

Litan Yan; Xianye Yu

doi:10.11948/2017036

2017 Volume 7 Issue 2

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Litan Yan, Xianye Yu. ON LP -SOLUTION OF FRACTIONAL HEAT EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 581-599. doi: 10.11948/2017036

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Litan Yan, Xianye Yu. ON L_P -SOLUTION OF FRACTIONAL HEAT EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 581-599. doi: 10.11948/2017036

ON L_P -SOLUTION OF FRACTIONAL HEAT EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION

Litan Yan^1,2,
Xianye Yu¹

1 College of Information Science and Technology, Donghua University 2999 North Renmin Rd. Songjiang, Shanghai 201620, China;
2 Department of Mathematics, College of Science, Donghua University, 2999 North Renmin Rd., Songjiang, Shanghai 201620, China

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Abstract

Abstract

In this paper, we study the fractional stochastic heat equation driven by fractional Brownian motions of the form du(t,x)= -(-∆)^α/2u(t,x) + f(t,x) dt + ∞ ???20170212??? k=1 g^k(t,x)δβ_t^k with u(0,x)=u₀, t ∈[0,T] and x ∈ R^d, where β^k={β_t^k,t ∈[0,T]},k ≥ 1 is a sequence of i.i.d. fractional Brownian motions with the same Hurst index H>1/2 and the integral with respect to fractional Brownian motion is Skorohod integral. By adopting the framework given by Krylov, we prove the existence and uniqueness of L_p-solution to such equation.
- Fractional Brownian motion /
- fractional heat equation /
- the LittlewoodPaley inequality
MSC: 60G22;60H15

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References

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