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Weak Versions of Stochastic Adams-Bashforth and Semi-implicit Leapfrog Schemes for SDEs
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Brian Ewald
Published/Copyright:
January 1, 2012
Abstract
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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Keywords for this article
stochastic differential equations;
numerical methods;
weak schemes;
multi-step schemes
Articles in the same Issue
- Efficient Preconditioners for Large Scale Binary Cahn-Hilliard Models
- Weak Versions of Stochastic Adams-Bashforth and Semi-implicit Leapfrog Schemes for SDEs
- A Quadratic Convergence Yielding Iterative Method for Nonlinear Ill-posed Operator Equations
- Exponentially Convergent Functional-discrete Method for Eigenvalue Transmission Problems with a Discontinuous Flux and the Potential as a Function in the Space L_1
- A FETI-DP Method for Crouzeix-Raviart Finite Element Discretizations
- An Approximation Method Based on Matrix Formulated Algorithm for the Heat Equation with Nonlocal Boundary Conditions
- Error Estimates for Approximations of American Put Option Price
