Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A second-order discretization for degenerate systems of stochastic differential equations
AU - Iguchi, Yuga
AU - Yamada, Toshihiro
PY - 2021/10/31
Y1 - 2021/10/31
N2 - The paper proposes a new second-order weak approximation scheme for hypoelliptic diffusions or degenerate systems of stochastic differential equations satisfying a certain Hörmander condition. The scheme is constructed by a Gaussian process and a stochastic polynomial weight through a technique based on Malliavin calculus, and is implemented by a Monte Carlo method and a quasi-Monte Carlo method. A variance analysis for the Monte Carlo method is discussed, and further control variate methods are introduced to reduce the variance. The effectiveness of the proposed scheme is illustrated through numerical experiments for some hypoelliptic diffusions.
AB - The paper proposes a new second-order weak approximation scheme for hypoelliptic diffusions or degenerate systems of stochastic differential equations satisfying a certain Hörmander condition. The scheme is constructed by a Gaussian process and a stochastic polynomial weight through a technique based on Malliavin calculus, and is implemented by a Monte Carlo method and a quasi-Monte Carlo method. A variance analysis for the Monte Carlo method is discussed, and further control variate methods are introduced to reduce the variance. The effectiveness of the proposed scheme is illustrated through numerical experiments for some hypoelliptic diffusions.
U2 - 10.1093/imanum/draa039
DO - 10.1093/imanum/draa039
M3 - Journal article
VL - 41
SP - 2782
EP - 2829
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
SN - 0272-4979
IS - 4
ER -