SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index

Luca M. Giordano; Maria Jolis; Lluís Quer-Sardanyons

SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index

Luca M. Giordano, Maria Jolis, Lluís Quer-Sardanyons^*

^*Autor corresponent d’aquest treball

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In this article, we consider the one-dimensional stochastic wave and heat equations driven by a linear multiplicative Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index [Formula presented]. We prove that the solution of each of the above equations is continuous in terms of the index H, with respect to the convergence in law in the space of continuous functions. The proof is based on a tightness criterion on the plane and Malliavin calculus techniques in order to identify the limit law.

Idioma original	English
Pàgines (de-a)	7396-7430
Nombre de pàgines	35
Revista	Stochastic Processes and their Applications
Volum	130
Número	12
Estat de la publicació	Publicada - de des. 2020

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https://ddd.uab.cat/record/274592

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Modelos estocásticos y aplicaciones
Bardina Simorra, X. (Investigador/a principal), Rovira Escofet, C. (Investigador/a Principal 2), Delgado de la Torre, R. (Investigador/a), Jolis Gimenez, M. (Investigador/a), Márquez Carreras, D. (Investigador/a), Quer Sardanyons, L. A. (Investigador/a) & Binotto ., G. (Col.laborador/a)
Ministerio de Ciencia e Innovación (MICINN)
1/01/19 → 30/09/22
Projecte: Projectes i Ajuts a la Recerca

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title = "SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index",

abstract = "In this article, we consider the one-dimensional stochastic wave and heat equations driven by a linear multiplicative Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index [Formula presented]. We prove that the solution of each of the above equations is continuous in terms of the index H, with respect to the convergence in law in the space of continuous functions. The proof is based on a tightness criterion on the plane and Malliavin calculus techniques in order to identify the limit law.",

keywords = "Fractional noise, Stochastic heat equation, Stochastic wave equation, Weak convergence, Wiener Chaos expansion",

author = "Giordano, {Luca M.} and Maria Jolis and Llu{\'i}s Quer-Sardanyons",

note = "Funding Information: The authors thank the anonymous referees for a careful reading of the manuscript. Research supported by the grants MTM2015-67802P and PGC2018-097848-B-I00 ( Ministerio de Econom{\'i}a y Competitividad, Spain ). Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

month = dec,

language = "English",

volume = "130",

pages = "7396--7430",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

number = "12",

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TY - JOUR

T1 - SPDEs with linear multiplicative fractional noise

T2 - Continuity in law with respect to the Hurst index

AU - Giordano, Luca M.

AU - Jolis, Maria

AU - Quer-Sardanyons, Lluís

N1 - Funding Information: The authors thank the anonymous referees for a careful reading of the manuscript. Research supported by the grants MTM2015-67802P and PGC2018-097848-B-I00 ( Ministerio de Economía y Competitividad, Spain ). Publisher Copyright: © 2020 Elsevier B.V.

PY - 2020/12

Y1 - 2020/12

N2 - In this article, we consider the one-dimensional stochastic wave and heat equations driven by a linear multiplicative Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index [Formula presented]. We prove that the solution of each of the above equations is continuous in terms of the index H, with respect to the convergence in law in the space of continuous functions. The proof is based on a tightness criterion on the plane and Malliavin calculus techniques in order to identify the limit law.

AB - In this article, we consider the one-dimensional stochastic wave and heat equations driven by a linear multiplicative Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index [Formula presented]. We prove that the solution of each of the above equations is continuous in terms of the index H, with respect to the convergence in law in the space of continuous functions. The proof is based on a tightness criterion on the plane and Malliavin calculus techniques in order to identify the limit law.

KW - Fractional noise

KW - Stochastic heat equation

KW - Stochastic wave equation

KW - Weak convergence

KW - Wiener Chaos expansion

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M3 - Article

AN - SCOPUS:85090148811

SN - 0304-4149

VL - 130

SP - 7396

EP - 7430

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 12

ER -

SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index

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