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Licensed Unlicensed Requires Authentication Published by De Gruyter January 1, 2012

Weak Versions of Stochastic Adams-Bashforth and Semi-implicit Leapfrog Schemes for SDEs

Brian Ewald


We consider the weak analogues of certain strong stochastic numerical schemes, namely an Adams-Bashforth scheme and a semi-implicit leapfrog scheme. We show that the weak version of the Adams-Bashforth scheme converges weakly with order 2, and the weak version of the semi-implicit leapfrog scheme converges weakly with order 1. We also note that the weak schemes are computationally simpler and easier to implement than the corresponding strong schemes, resulting in savings in both programming and computational effort.

Received: 2011-01-28
Revised: 2011-02-01
Accepted: 2011-08-07
Published Online: 2012
Published in Print: 2012

© Institute of Mathematics, NAS of Belarus

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