Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs

Xavier Bardina; Juan Pablo Márquez; Lluís Quer-Sardanyons

Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs

Xavier Bardina, Juan Pablo Márquez, Lluís Quer-Sardanyons^*

^*Corresponding author for this work

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

2 Citations (Scopus)

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Abstract

We consider a Lévy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a semilinear one-dimensional stochastic heat equation driven by the space–time white noise.

Original language	English
Pages (from-to)	5735-5767
Number of pages	33
Journal	Stochastic Processes and their Applications
Volume	130
Issue number	9
Publication status	Published - Sept 2020

Keywords

Brownian sheet
Lévy sheet
Stochastic heat equation
Weak approximation

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Cite this

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title = "Weak approximation of the complex Brownian sheet from a L{\'e}vy sheet and applications to SPDEs",

abstract = "We consider a L{\'e}vy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a semilinear one-dimensional stochastic heat equation driven by the space–time white noise.",

keywords = "Brownian sheet, L{\'e}vy sheet, Stochastic heat equation, Weak approximation",

author = "Xavier Bardina and M{\'a}rquez, {Juan Pablo} and Llu{\'i}s Quer-Sardanyons",

note = "Funding Information: Research supported by the grant PGC2018-097848-B-I00 of the Ministerio de Econom{\'i}a y Competitividad, Spain . J.P. M{\'a}rquez was supported by a fellowship of CONACYT-M{\'e}xico . Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

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language = "English",

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pages = "5735--5767",

journal = "Stochastic Processes and their Applications",

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T1 - Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs

AU - Bardina, Xavier

AU - Márquez, Juan Pablo

AU - Quer-Sardanyons, Lluís

N1 - Funding Information: Research supported by the grant PGC2018-097848-B-I00 of the Ministerio de Economía y Competitividad, Spain . J.P. Márquez was supported by a fellowship of CONACYT-México . Publisher Copyright: © 2020 Elsevier B.V.

PY - 2020/9

Y1 - 2020/9

N2 - We consider a Lévy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a semilinear one-dimensional stochastic heat equation driven by the space–time white noise.

AB - We consider a Lévy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a semilinear one-dimensional stochastic heat equation driven by the space–time white noise.

KW - Brownian sheet

KW - Lévy sheet

KW - Stochastic heat equation

KW - Weak approximation

UR - http://www.scopus.com/inward/record.url?scp=85084233108&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85084233108

SN - 0304-4149

VL - 130

SP - 5735

EP - 5767

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 9

ER -

Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs

Abstract

Keywords

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