@Article{IJNAM-2-197,
author = {Schurz , Henri},
title = {Convergence and Stability of Balanced Implicit Methods for Systems of SDEs},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2005},
volume = {2},
number = {2},
pages = {197--220},
abstract = {<p style="text-align: justify;">Several convergence and stability issues of the balanced
implicit methods (BIMs) for systems of real-valued ordinary stochastic
differential equations are thoroughly discussed. These methods are
linear-implicit ones, hence easily implementable and computationally
more efficient than commonly known nonlinear-implicit methods. In
particular, we relax the so far known convergence condition on its
weight matrices $c^j$. The presented convergence proofs extend to the
case of nonrandom variable step sizes and show a dependence on certain
Lyapunov-functionals $V$ : $\rm{IR}^d \rightarrow \rm{IR}_+^1$. The proof of $L^2$-convergence with
global rate 0.5 is based on the stochastic Kantorovich-Lax-Richtmeyer
principle proved by the author (2002). Eventually, $p$-th mean stability
and almost sure stability results for martingale-type test equations
document some advantage of BlMs. The problem of weak convergence with
respect to the test class $C_{b(\kappa)}^2 (\rm{IR}^d, \rm{IR}^1)$ and with global rate 1.0
is tackled too.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/929.html}
}