Article2004

Cubature on Wiener space

196 citations0/0 files storedProceedings of the Royal Society A Mathematical Physical and Engineering Sciences

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Stochastic processes and financial applications Numerical methods for differential equations Mathematical Approximation and Integration

Abstract

It is well known that there is a mathematical equivalence between ‘solving’ parabolic partial differential equations (PDEs) and ‘the integration’ of certain functionals on Wiener space. Monte Carlo simulation of stochastic differential equations (SDEs) is a naive approach based on this underlying principle. In finite dimensions, it is well known that cubature can be a very effective approach to integration. We discuss the appropriate extension of this idea to Wiener space. In the process we develop high–order numerical schemes valid for high–dimensional SDEs and semi–elliptic PDEs.

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References

2016Numerical solution of stochastic differential equations 1983Stochastic Differential Equations and Diffusion Processes 1998Differential equations driven by rough signals 1997Stochastic Analysis

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