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Numerical Integration Of Stochastic Differential Equations by G. N. Milʹshteĭn

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1Numerical Integration Of Stochastic Differential Equations

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Numerical algorithms for the integration of stochastic differential equations in the presence of white noise are introduced and compared. Algorithms for the integration of stochastic correlated forces are also briefly reviewed. Finally, a specialised algorithm for two dimensional systems is derived, having in mind the integration of particles in the liquid state.

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2A Comparison Of A Few Numerical Schemes For The Integration Of Stochastic Differential Equations In The Stratonovich Interpretation

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Three schemes, whose expressions are not too complex, are selected for the numerical integration of a system of stochastic differential equations in the Stratonovich interpretation: the integration methods of Heun, Milstein, and derivative-free Milstein. The strong (path-wise) convergence is studied for each method by comparing the final points after integrating with $2^n$ and $2^{n-1}$ time steps. We also compare the time that the computer takes to carry out the integration with each scheme. Putting both things together, we conclude that, at least for our system, the Heun method is by far the best performing one.

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The book is available for download in "texts" format, the size of the file-s is: 7.55 Mbs, the file-s for this book were downloaded 102 times, the file-s went public at Wed Sep 18 2013.

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3BSTJ 60: 8. October 1981: Numerical Integration Of Stochastic Differential Equations - II. (Greenside, H.S.; Helfand, E. )

Bell System Technical Journal, 60: 8. October 1981 pp 1927-1940. Numerical Integration of Stochastic Differential Equations - II. (Greenside, H.S.; Helfand, E. )

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  • Title: ➤  BSTJ 60: 8. October 1981: Numerical Integration Of Stochastic Differential Equations - II. (Greenside, H.S.; Helfand, E. )
  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 9.53 Mbs, the file-s for this book were downloaded 429 times, the file-s went public at Sat Jan 19 2013.

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4BSTJ 58: 10. December 1979: Numerical Integration Of Stochastic Differential Equations. (Helfand, E.)

Bell System Technical Journal, 58: 10. December 1979 pp 2289-2299. Numerical Integration of Stochastic Differential Equations. (Helfand, E.)

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  • Title: ➤  BSTJ 58: 10. December 1979: Numerical Integration Of Stochastic Differential Equations. (Helfand, E.)
  • Language: English

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The book is available for download in "texts" format, the size of the file-s is: 8.13 Mbs, the file-s for this book were downloaded 417 times, the file-s went public at Sat Jan 19 2013.

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