Families of efficient second order Runge–Kutta methods for the weak approximation of Itô stochastic differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2008.03.012 ◽

2009 ◽

Vol 59 (3-4) ◽

pp. 582-594 ◽

Author(s):

Kristian Debrabant ◽

Andreas Rößler

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Second Order ◽

Weak Approximation ◽

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New explicit stabilized stochastic Runge-Kutta methods with weak second order for stiff Itô stochastic differential equations

Numerical Algorithms ◽

10.1007/s11075-018-0615-y ◽

2018 ◽

Vol 82 (2) ◽

pp. 593-604

Author(s):

Xiao Tang ◽

Aiguo Xiao

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Second Order ◽

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Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations

Stochastic Analysis and Applications ◽

10.1080/07362990500397699 ◽

2006 ◽

Vol 24 (1) ◽

pp. 97-134 ◽

Author(s):

Andreas Rößler

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Rooted Tree ◽

Order Conditions ◽

Weak Approximation ◽

Tree Analysis ◽

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A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method

Finance and Stochastics ◽

10.1007/s00780-009-0101-4 ◽

2009 ◽

Vol 13 (3) ◽

pp. 415-443 ◽

Author(s):

Mariko Ninomiya ◽

Syoiti Ninomiya

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Approximation Scheme ◽

Higher Order ◽

Weak Approximation ◽

Kutta Method ◽

Runge Kutta Method ◽

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Weak first- or second-order implicit Runge–Kutta methods for stochastic differential equations with a scalar Wiener process

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2007.06.024 ◽

2008 ◽

Vol 217 (1) ◽

pp. 166-179 ◽

Author(s):

Yoshio Komori

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Wiener Process ◽

Second Order ◽

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Second Order Runge–Kutta Methods for Itô Stochastic Differential Equations

SIAM Journal on Numerical Analysis ◽

10.1137/060673308 ◽

2009 ◽

Vol 47 (3) ◽

pp. 1713-1738 ◽

Author(s):

Andreas Rößler

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Second Order ◽

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Mean-square stability of second-order Runge–Kutta methods for stochastic differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2004.05.019 ◽

2005 ◽

Vol 175 (2) ◽

pp. 355-367 ◽

Author(s):

A. Tocino

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Second Order ◽

Mean Square ◽

Mean Square Stability ◽

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Supplement: Efficient weak second order stochastic Runge–Kutta methods for non-commutative Stratonovich stochastic differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2011.04.021 ◽

2011 ◽

Vol 235 (17) ◽

pp. 5326-5329 ◽

Author(s):

Yoshio Komori ◽

Kevin Burrage

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Second Order ◽

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A class of second-order Runge-Kutta methods for numerical solution of stochastic differential equations

Stochastic Analysis and Applications ◽

10.1080/07362999808809575 ◽

1998 ◽

Vol 16 (6) ◽

pp. 977-991 ◽

Author(s):

M.I. Abukhaled ◽

E.J. Allen

Keyword(s):

Differential Equations ◽

Numerical Solution ◽

Stochastic Differential Equations ◽

Second Order ◽

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Weak second-order stochastic Runge–Kutta methods for non-commutative stochastic differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2006.06.006 ◽

2007 ◽

Vol 206 (1) ◽

pp. 158-173 ◽

Author(s):

Yoshio Komori

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Second Order ◽

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Numerical solution of stochastic differential equations by second order Runge–Kutta methods

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2011.01.018 ◽

2011 ◽

Vol 53 (9-10) ◽

pp. 1910-1920 ◽

Author(s):

M. Khodabin ◽

K. Maleknejad ◽

M. Rostami ◽

M. Nouri

Keyword(s):

Differential Equations ◽

Numerical Solution ◽

Stochastic Differential Equations ◽

Second Order ◽

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