Kpz equation with fractional derivatives of white noise

Masato Hoshino

doi:10.1007/s40072-016-0078-x

Kpz equation with fractional derivatives of white noise

Masato Hoshino

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	827-890
Number of pages	64
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	4
Issue number	4
DOIs	https://doi.org/10.1007/s40072-016-0078-x
Publication status	Published - Dec 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1007/s40072-016-0078-x

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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.

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Kpz equation with fractional derivatives of white noise

Abstract

All Science Journal Classification (ASJC) codes

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