Optimal Regularity of Stochastic Evolution Equations in M-type 2 Banach Spaces

Chuying Huang; Jialin Hong; Zhihui Liu

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Optimal Regularity of Stochastic Evolution Equations in M-type 2 Banach Spaces

Jialin Hong, Chuying Huang, Zhihui Liu

Probability · Submitted 25 Sep 2017

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The authors' main claim In this paper, we prove the well-posedness and op- timal trajectory regularity for the solution of stochastic evolution equations driven by general multiplicative noises in martingale type 2 Banach spaces.

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arXiv ID1709.08472 (version 1)

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CitationChuying Huang, Jialin Hong, Zhihui Liu. "Optimal Regularity of Stochastic Evolution Equations in M-type 2 Banach Spaces." arXiv:1709.08472 (2017). https://pith.science/paper/W2TAFFS7

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In this paper, we prove the well-posedness and op- timal trajectory regularity for the solution of stochastic evolution equations driven by general multiplicative noises in martingale type 2 Banach spaces. The main idea of our method is to combine the approach in [HL] dealing with Hilbert setting and a version of Burkholder inequality in M-type 2 Banach space. Applying our main results to the stochastic heat equation gives a positive an- swer to an open problem proposed in [JR12].

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper, we prove the well-posedness and op- timal trajectory regularity for the solution of stochastic evolution equations driven by general multiplicative noises in martingale type 2 Banach spaces.	contribution 0.53	0.96	0.92	asserted 1.00
s1	The main idea of our method is to combine the approach in [HL] dealing with Hilbert setting and a version of Burkholder inequality in M-type 2 Banach space.	method 1.00	0.67	0.05	asserted 1.00
s2	Applying our main results to the stochastic heat equation gives a positive an- swer to an open problem proposed in [JR12].	result 0.61	0.89	0.17	asserted 1.00

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Original abstract

In this paper, we prove the well-posedness and op- timal trajectory regularity for the solution of stochastic evolution equations driven by general multiplicative noises in martingale type 2 Banach spaces. The main idea of our method is to combine the approach in [HL] dealing with Hilbert setting and a version of Burkholder inequality in M-type 2 Banach space. Applying our main results to the stochastic heat equation gives a positive an- swer to an open problem proposed in [JR12].

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Applying the Gronwall's inequality in [ref] and the uniform boundedness [ref], we get [ref].

Well-posedness and Optimal Regularity of Stochastic Evolution Equations with Multiplicative Noises · Well-posedness · 0.84

Cites as support 1 paper

On the other hand, some error estimations in numerical analysis and simulation of Eq. [ref] can also be improved (see, e.g., [ref] ).

Weak convergence rates for numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients in UMD Banach spaces · Introduction · 0.96

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Liu [ref] and references therein.

Well-posedness and Optimal Regularity of Stochastic Evolution Equations with Multiplicative Noises · Introduction · 0.83

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