Convergence rate of strong approximations of compound random maps, application to spdes

Emmanuel Gobet; Mohamed Mrad

doi:10.3934/dcdsb.2018171

Convergence rate of strong approximations of compound random maps, application to spdes

Emmanuel Gobet
, Mohamed Mrad

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

Abstract

We consider a random map x ? F(?, x) and a random variable T(?), and we denote by F^N(?, x) and T^N(?) their approximations: We establish a strong convergence result, in Lp-norms, of the compound approximation F^N(?, T^N(?)) to the compound variable F(?, T(?)), in terms of the approximations of F and T. We then apply this result to the composition of two Stochastic Differential Equations (SDEs) through their initial conditions, which can give a way to solve some Stochastic Partial Differential Equations (SPDEs), in particular those from stochastic utilities.

Original language	English
Pages (from-to)	4455-4476
Number of pages	22
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	23
Issue number	10
DOIs	https://doi.org/10.3934/dcdsb.2018171
Publication status	Published - 1 Dec 2018
Externally published	Yes

Keywords

Euler scheme
Garsia-Rodemich-Rumsey lemma
SPDE
Stochastic flow
Strong approximation

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10.3934/dcdsb.2018171

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abstract = "We consider a random map x ? F(?, x) and a random variable T(?), and we denote by FN(?, x) and TN(?) their approximations: We establish a strong convergence result, in Lp-norms, of the compound approximation FN(?, TN(?)) to the compound variable F(?, T(?)), in terms of the approximations of F and T. We then apply this result to the composition of two Stochastic Differential Equations (SDEs) through their initial conditions, which can give a way to solve some Stochastic Partial Differential Equations (SPDEs), in particular those from stochastic utilities.",

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T1 - Convergence rate of strong approximations of compound random maps, application to spdes

AU - Gobet, Emmanuel

AU - Mrad, Mohamed

PY - 2018/12/1

Y1 - 2018/12/1

N2 - We consider a random map x ? F(?, x) and a random variable T(?), and we denote by FN(?, x) and TN(?) their approximations: We establish a strong convergence result, in Lp-norms, of the compound approximation FN(?, TN(?)) to the compound variable F(?, T(?)), in terms of the approximations of F and T. We then apply this result to the composition of two Stochastic Differential Equations (SDEs) through their initial conditions, which can give a way to solve some Stochastic Partial Differential Equations (SPDEs), in particular those from stochastic utilities.

AB - We consider a random map x ? F(?, x) and a random variable T(?), and we denote by FN(?, x) and TN(?) their approximations: We establish a strong convergence result, in Lp-norms, of the compound approximation FN(?, TN(?)) to the compound variable F(?, T(?)), in terms of the approximations of F and T. We then apply this result to the composition of two Stochastic Differential Equations (SDEs) through their initial conditions, which can give a way to solve some Stochastic Partial Differential Equations (SPDEs), in particular those from stochastic utilities.

KW - Euler scheme

KW - Garsia-Rodemich-Rumsey lemma

KW - SPDE

KW - Stochastic flow

KW - Strong approximation

UR - https://www.scopus.com/pages/publications/85054197460

U2 - 10.3934/dcdsb.2018171

DO - 10.3934/dcdsb.2018171

M3 - Article

AN - SCOPUS:85054197460

SN - 1531-3492

VL - 23

SP - 4455

EP - 4476

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 10

ER -

Convergence rate of strong approximations of compound random maps, application to spdes

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Keywords

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