Abstract
Mathematicians often face the question to which extent mathematical models describe processes of the real world. These models are derived from experimental data, hence they describe real phenomena only approximately. Thus a mathematical approach must begin with choosing properties which are not very sensitive to small changes in the model, and so may be viewed as properties of the real process. In particular, this concerns real processes which can be described by means of ordinary differential equations. By this reason different notions of stability played an important role in the qualitative theory of ordinary differential equations commonly known nowdays as the theory of dynamical systems. Since physical processes are usually affected by an enormous number of small external fluctuations whose resulting action would be natural to consider as random, the stability of dynamical systems with respect to random perturbations comes into the picture. There are differences between the study of stability properties of single trajectories, i.e., the Lyapunov stability, and the global stability of dynamical systems. The stochastic Lyapunov stability was dealt with in Hasminskii [Has].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Birkhäuser Boston
About this chapter
Cite this chapter
Kifer, Y. (1988). Introduction. In: Random Perturbations of Dynamical Systems. Progress in Probability and Statistics, vol 16. Birkhäuser Boston. https://doi.org/10.1007/978-1-4615-8181-9_1
Download citation
DOI: https://doi.org/10.1007/978-1-4615-8181-9_1
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4615-8183-3
Online ISBN: 978-1-4615-8181-9
eBook Packages: Springer Book Archive