A Galerkin approximation scheme for the mean correction in a meanreversion stochastic differential equation
Wu, JiangLun and Yang, Wei (2013) A Galerkin approximation scheme for the mean correction in a meanreversion stochastic differential equation. Preprint / Working Paper. UNSPECIFIED.
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Abstract
This paper is concerned with the following Markovian stochastic dierential equation of meanreversion type dRt = ( + (Rt; t))Rtdt + RtdBt with an initial value R0 = r0 2 R, where 2 R and > 0 are constants, and the mean correction function : R [0; 1) 7! (x; t) 2 R is twice continuously dierentiable in x and continuously dierentiable in t. We rst derive that under the assumption of path indepen dence of the density process of Girsanov transformation for the above stochastic dierential equation, the mean correction function sat ises a nonlinear partial dierential equation which is known as the viscous Burgers equation. We then develop a Galerkin type approxi mation scheme for the function by utilizing truncation of discretised Fourier transformation to the viscous Burgers equation.


Item type: Monograph(Preprint / Working Paper) ID code: 43822 Dates: DateEvent2013PublishedKeywords: galerkin approximation scheme, mean correction, stochastic differential equation, meanreversion, markovian stochastic differential equation of meanrevision type, viscous burgers equation, truncation of (discretised) fourier transformation, numerical approximation scheme, Mathematics Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 15 May 2013 15:58 Last modified: 25 May 2022 08:04 URI: https://strathprints.strath.ac.uk/id/eprint/43822