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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
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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

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