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Journal article
Fractional stochastic wave equation driven by a Gaussian noise rough in space
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, v 26(4), pp 2699-2726
01 Nov 2020
Abstract
In this article, we consider fractional stochastic wave equations on R driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter H is an element of (1/4, 1/2) in space. We prove the existence and uniqueness of the mild Skorohod solution, establish lower and upper bounds for the pth moment of the solution for all p <= 2, and obtain the Holder continuity in time and space variables for the solution.
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Details
- Title
- Fractional stochastic wave equation driven by a Gaussian noise rough in space
- Creators
- Jian Song - Shandong Univ, Res Ctr Math & Interdisciplinary Sci, Qingdao 266237, Shandong, Peoples R ChinaXiaoming Song - Drexel UniversityFangjun Xu - East China Normal Univ, Key Lab Adv Theory & Applicat Stat & Data Sci MOE, Sch Stat, Shanghai 200062, Peoples R China
- Publication Details
- Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, v 26(4), pp 2699-2726
- Publisher
- Int Statistical Inst
- Number of pages
- 28
- Grant note
- B14019 / 111 Project; Ministry of Education, China - 111 Project 11871219; 11871220 / National Natural Science Foundation of China; National Natural Science Foundation of China (NSFC)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000563380300009
- Scopus ID
- 2-s2.0-85091251163
- Other Identifier
- 991019167334904721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Statistics & Probability