Humboldt Universität zu
Berlin 
Institut für
Mathematik
Stochastik
und Finanzmathematik
Publications of Evelyn
Buckwar
Submitted
- (with J.A.D. Appleby) Sufficient
conditions
for
polynomial asymptotic behaviour of the stochastic pantograph equation. Preprint(gzipped)
- (with R. Kuske, S.-E.A. Mohammed and T. Shardlow) The weak Euler
scheme for stochastic differential delay equations. Preprint
(PDF-file).
- (with A. Rößler and R. Winkler)
Stochastic Runge-Kutta methods for Itô-SODEs with small noise.
Published Articles
- Numerical Treatment of a Non-uniquely
Solvable Volterra
Integral Equation, Proceedings of 15th IMACS World Congress on
Scientific
Computation, Modelling, and Applied Mathematics (Achim Sydov, editor), Vol.
2, 439-444, 1997.
- (with Y. Luchko) Invariance
of a Partial Differential Equation of Fractional Order under the Lie
Group
of Scaling Transformations (gzipped)
appeared
in Journal of Mathematical Analysis and Applications 277,
81-97, 1998.
- On a Nonlinear Volterra Integral Equation Proceedings
of the Volterra Centennial Symposium, Arlington, Texas, USA, 23.- 25.5.
1996 (eds: C. Corduneanu and I.W.Sandberg) Gordon and Breach
Science
Publishers, 2000.
- Introduction to the Numerical Analysis of
Stochastic
Delay Differential Equations, Journal of Computational and Applied
Mathematics 125,
297--307, 2000. JCAM
*
- Introduction to the Numerical Analysis of
Stochastic
Delay Differential Equations, Proceedings of Equadiff 99, Editors:
B.
Fiedler, K. Groeger und J. Sprekels , 1021--1023, 2000.
- (with CTH Baker) Numerical Analysis of
Explicit One-step
Methods for Stochastic Delay Differential Equations, LMS-Journal of
Computational Mathematics, 3 , 315--335, 2000. LMS-JCM
*
- (with CTH Baker) Continuous Theta-methods
for
the
Stochastic Pantograph Equation, Electronic Transactions on
Numerical
Analysis , 11 , 131--151, 2000. ETNA
*
- The $\Theta$-Maruyama scheme for
stochastic
functional differential equations with distributed memory term. Monte
Carlo Methods and Applications Vol.10, No.3-4, 235--244, 2004. Preprint(gzipped)
- (with R. Winkler) On Two-step Schemes for
SDEs with Small Noise. PAMM Proc.
Appl. Math. Mech. 4,
15--18, 2004.
- (with T. Shardlow) Weak
approximation of stochastic
differential delay equations.(PDF), IMA J.
Numerical
Analysis, 25, 57--86, 2005.
- (with CTH Baker) On Halanay-type analysis of exponential
stability for the $\theta$--Maruyama method for stochastic delay
differential equations. Preprint
(gzipped). Stochastics
& Dynamics 5(2),
201-209, 2005.
- (with CTH
Baker) Exponential stability in
p-th
mean of solutions, and of convergent Euler-type solutions, of
stochastic
delay differential equations. Preprint(gzipped).
Journal of Computational
and Applied
Mathematics, 184
(2), 404--427, 2005.
- (with J.A.D. Appleby) Noise Induced
Oscillation
in Solutions
of Stochastic Delay Differential Equations. Preprint(gzipped).
Dynamic Systems and Applications
14(2), 175--196, 2005.
- Existence and Uniqueness of Solutions of Abel Integral Equations
with Power-law Non-linearities. Nonlinear
Analysis 63(1), 88--96, 2005.
- One-step
approximations for stochastic
functional differential equations. Preprint(gzipped),
Applied Numerical
Mathematics 56(5), 667--681, 2006.
- (with R. Kuske, B. L'Esperance and T. Soo)
Noise-sensitivity in
machine tool vibrations. Preprint
(PDF-file). Accepted in International
Journal of Bifurcations and Chaos.
- (with R. Winkler) Multi-step
methods for SDEs and their application to problems with small
noise. Preprint (PDF-file), SINUM 44
(2), 779--803, 2006.
- (with R. Horvath Bokor and R. Winkler)
Asymptotic
mean-square stability of two-step methods for
stochastic ordinary differential equations, Preprint
04-25 (PDF-file), BIT Numerical Mathematics 46(2), 261 - 282, 2006.
- (with R. Winkler) Improved linear multi-step methods for
stochastic ordinary differential equations. Preprint
(PDF-file). Journal
of Computational
and Applied
Mathematics, 205 (2), 912--922, 2007.
- (with R. Winkler) Multi-step Maruyama methods for stochastic
delay differential equations. Preprint
(PDF-file). Accepted for Stochastic
Analysis and Applications.
* Unfortunately none of the websites let me set a direct link to the
location
of the article.
Habilitation
Numerical analysis for stochastic ordinary and
functional differential equations. (Submitted July 2004, defended
December 2004 )
Thesis
Iterative Approximation of the Positive Solutions of a Class of
Nonlinear
Volterra-type Integral Equations. Logos-Verlag, Berlin, 1997.