A Galerkin approximation scheme for the mean correction in a mean-reversion stochastic differential equation

JiangLun Wu, Wei Yang

Research output: Working paper

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Abstract

This paper is concerned with the following Markovian stochastic
dierential equation of mean-reversion 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 non-linear 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.
Original languageEnglish
Number of pages16
Publication statusPublished - 2013

Keywords

  • galerkin approximation scheme
  • mean correction
  • stochastic differential equation
  • mean-reversion
  • markovian stochastic differential equation of mean-revision type
  • viscous burgers equation
  • truncation of (discretised) fourier transformation
  • numerical approximation scheme

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