### 抄録

In this paper, we consider the KPZ equation driven by space-time white noise replaced with its fractional derivatives of order γ > 0 in spatial variable. A well-posedness theory for the KPZ equation is established by Hairer (Invent Math 198:269–504, 2014) as an application of the theory of regularity structures. Our aim is to see to what extent his theory works if noises become rougher. We can expect that his theory works if and only if γ < 1/2. However, we show that the renormalization like “(∂
_{x}
h)
^{2}
− ∞” is well-posed only if γ < 1/4.

元の言語 | 英語 |
---|---|

ページ（範囲） | 827-890 |

ページ数 | 64 |

ジャーナル | Stochastics and Partial Differential Equations: Analysis and Computations |

巻 | 4 |

発行部数 | 4 |

DOI | |

出版物ステータス | 出版済み - 1 1 2016 |

外部発表 | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics

### これを引用

**Kpz equation with fractional derivatives of white noise.** / Hoshino, Masato.

研究成果: ジャーナルへの寄稿 › 記事

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TY - JOUR

T1 - Kpz equation with fractional derivatives of white noise

AU - Hoshino, Masato

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this paper, we consider the KPZ equation driven by space-time white noise replaced with its fractional derivatives of order γ > 0 in spatial variable. A well-posedness theory for the KPZ equation is established by Hairer (Invent Math 198:269–504, 2014) as an application of the theory of regularity structures. Our aim is to see to what extent his theory works if noises become rougher. We can expect that his theory works if and only if γ < 1/2. However, we show that the renormalization like “(∂ x h) 2 − ∞” is well-posed only if γ < 1/4.

AB - In this paper, we consider the KPZ equation driven by space-time white noise replaced with its fractional derivatives of order γ > 0 in spatial variable. A well-posedness theory for the KPZ equation is established by Hairer (Invent Math 198:269–504, 2014) as an application of the theory of regularity structures. Our aim is to see to what extent his theory works if noises become rougher. We can expect that his theory works if and only if γ < 1/2. However, we show that the renormalization like “(∂ x h) 2 − ∞” is well-posed only if γ < 1/4.

UR - http://www.scopus.com/inward/record.url?scp=85038426217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038426217&partnerID=8YFLogxK

U2 - 10.1007/s40072-016-0078-x

DO - 10.1007/s40072-016-0078-x

M3 - Article

AN - SCOPUS:85038426217

VL - 4

SP - 827

EP - 890

JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

SN - 2194-0401

IS - 4

ER -