13. chen.hu.ea:18:intermittency

Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise

Le Chen, Yaozhong Hu, Kamran Kalbasi, and David Nualart

Abstract: This paper studies the stochastic heat equation driven by time fractional Gaussian noise with Hurst parameter \(H\in (0,1/2)\). We establish the Feynman-Kac representation of the solution and use this representation to obtain matching lower and upper bounds for the \(L^p(\Omega)\) moments of the solution.

MSC 2010 subject classifications: Primary 60H15. Secondary 60G60, 35R60.

Keywords: stochastic heat equation, Feynman-Kac integral, Feynman-Kac formula, time fractional Gaussian noise, fractional calculus, moment bounds, Lyapunov exponents, intermittency.

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[CHSS18] Chen, Le, Hu, Yaozhong, Kalbasi, Kamran & Nualart, David (2018) ‘Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise’, Probab. Theory Related Fields 171, 431–457. <https://doi.org/10.1007/s00440-017-0783-z>

@article{chen.hu.ea:18:intermittency,
  author        = {Chen, Le and Hu, Yaozhong and Kalbasi, Kamran and Nualart, David},
  title         = {Intermittency for the stochastic heat equation driven by a rough time fractional {G}aussian noise},
  journal       = {Probab. Theory Related Fields},
  fjournal      = {Probability Theory and Related Fields},
  volume        = {171},
  year          = {2018},
  number        = {1-2},
  pages         = {431--457},
  issn          = {0178-8051},
  mrclass       = {60H15 (35K15 35R60 60G60)},
  mrnumber      = {3800837},
  mrreviewer    = {Isamu D\^{o}ku},
  doi           = {10.1007/s00440-017-0783-z},
  url           = {https://doi.org/10.1007/s00440-017-0783-z}
}

References: Balan and Conus [BC16]; Bertini and Cancrini [BC95a]; Carmona and Molchanov [CM94]; Chen and Dalang [CD15b]; Chen et al. [CHN19]; Conus et al. [CJKS13b]; Foondun and Khoshnevisan [FK09]; Hu [Hu17]; Hu and Lê [HL17]; Hu et al. [HLN12]; Hu and Nualart [HN09]; Hu et al. [HNS09]; Hu et al. [HHNT15]; Kalbasi and Mountford [KM15]; Mémin et al. [MMV01]; Nualart [Nua06]; Olver et al. [OLBC10]; Pipiras and Taqqu [PT01]; Podlubny [Pod99]; Zeldovich et al. [ZRS90];

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