STOCHASTIC DIFFERENTIAL EQUATIONS
Stochastic differential equations arise in modelling a variety of
random dynamic phenomena in the physical, biological,
engineering and social sciences. Solutions of these
equations are often diffusion processes and hence are connected to the
subject of partial differential equations.
Chung, K. L., and Williams, R. J., Introduction to Stochastic
Integration, Second Edition, Birkhauser, 1990.
Karatzas, I. and Shreve, S., Brownian motion and stochastic
calculus, 2nd edition, Springer.
Metivier, M., Semimartingales, de Gruyter, Berlin, 1982.
Oksendal, B., Stochastic Differential Equations,
Springer, 5th edition.
Protter, P., Stochastic Integration and Differential
Revuz, D., and Yor, M., Continuous Martingales and Brownian Motion, Springer, Third Edition, 1999.
Rogers, L. C. G., and Williams, D., Diffusions, Markov Processes,
and Martingales, Wiley, Volume 1: 1994, Volume 2: 1987.
Jacod, J., and Shiryaev, A. N., Limit theorems for
stochastic processes, Springer-Verlag, 1987.
Numerical solution of SDEs
Talay, D., and Tubaro, L., Expansion of the global error
for numerical schemes solving stochastic differential equations,
Stochastic Analysis and Applications, 8 (1990), 94-120.
Kloeden, P. E., and Platen, E., Numerical
solution of stochastic differential equations,
Kloeden, P. E., Platen, E., and Schurz, H.,
Numerical solution of SDEs through computer experiments,
Bouleau, N., and Lepingle, D., Numerical Methods for Stochastic
Processes, Wiley, 1994.
Gaines, J. G., and Lyons, T. J., Variable step
size control in the numerical solution of
stochastic differential equations, SIAM J. Applied
Math., to appear.
SOFTWARE Symbolic Stochastic
Calculus Software developed by Wilfrid Kendall, University of Warwick. This
runs under Mathematica for example.
C programs for the numerical solution of
stochastic differential equations,
provided by Jessica Gaines, Edinburgh University, U.K.
Software for numerical study of the stochastic Brusselator (provided
by Gabriele Bleckert and Klaus Reiner Schenk-Hoppe).
Math 286 (Stochastic Differential
is offered by the UCSD Mathematics Department.
Please direct any questions to
Professor Ruth J. Williams, email:
STOCHASTIC DIFFERENTIAL EQUATIONS WORKSHOP WEB SITE AT UCSD
This post workshop web site (provided by the UCSD
Center for Magnetic Recording Research) has some useful links to
other sites associated with
SDEs, especially those associated with computation. >