Reliability and accuracy in the space Lp(T) for the calculation of integrals depending on a parameter by the Monte Carlo method

Yuriy V. Kozachenko; Yuriy Y. Mlavets

doi:10.1515/mcma-2015-0104

Published by De Gruyter September 1, 2015

Reliability and accuracy in the space L_p(T) for the calculation of integrals depending on a parameter by the Monte Carlo method

Yuriy V. Kozachenko and Yuriy Y. Mlavets

From the journal Monte Carlo Methods and Applications

https://doi.org/10.1515/mcma-2015-0104

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Abstract

This paper is devoted to the estimation of the accuracy and reliability (in L_p(T) metrics) for the calculation of improper integrals depending on a parameter t using the Monte Carlo method. For this estimates we use the theory of 𝐅_ψ(Ω) spaces.

Keywords: 𝐅ψ(Ω) space of random variables; condition 𝐇; Monte Carlo method; random process

MSC: 65C05; 60G07

Received: 2015-3-2

Accepted: 2015-8-12

Published Online: 2015-9-1

Published in Print: 2015-9-1

Reliability and accuracy in the space L_p(T) for the calculation of integrals depending on a parameter by the Monte Carlo method

Abstract

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