Hostname: page-component-6bf8c574d5-xtvcr Total loading time: 0 Render date: 2025-02-25T15:55:13.359Z Has data issue: false hasContentIssue false
  • English
  • Français

Taylor expansions for continuous Stieltjes differential equations

Published online by Cambridge University Press:  17 April 2009

P.E. Kloeden  and
J. Panadiwal
P.E. Kloeden
Affiliation:
School of Computing and Mathematics, Deakin University, Geelong Campus Geelong, Vic. 3217, Australia
J. Panadiwal
Affiliation:
School of Computing and Mathematics, Deakin University, Geelong Campus Geelong, Vic. 3217, Australia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The general structure of Taylor expansions of functions of solutions of continuous Stieltjes differential equations is established. A compact formalism involving hierarchical sets of multi-indices and their associated remainder sets is used. The corresponding multiple Riemann-Stieltjes integrals of time and of the driving functions in the Stieltjes terms of the differential equations, necessarily of bounded variation and continuous here, appear in the expansions and their remainders.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 325 - 336
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Groh, J., ‘A nonlinear Volterra-Stieltjes integral equation and a Gronwall inequality in one dimension’, Illinois J. Math. 24 (1980), 244–263.CrossRefGoogle Scholar
[2]Kloeden, P.E. and Platen, E., ‘Stratonovich and Ito stochastic Taylor expansions’, Math.Nachr. 151 (1991), 33–50.Google Scholar
[3]Pandit, S.G. and Deo, S.G., Differential equations involving impulses, Lecture Notes in Mathematics 954 (Springer-Verlag, Berlin, Heidelberg, New York, 1982).CrossRefGoogle Scholar
[4]Protter, M.H. and Morrey, C.B., A first course in real analysis (Springer-Verlag, Berlin, Heidelberg, New York, 1977).Google Scholar