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Taylor expansions for continuous Stieltjes differential equations

  • P.E. Kloeden (a1) and J. Panadiwal (a1)

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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.

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References

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[1]Groh, J., ‘A nonlinear Volterra-Stieltjes integral equation and a Gronwall inequality in one dimension’, Illinois J. Math. 24 (1980), 244263.
[2]Kloeden, P.E. and Platen, E., ‘Stratonovich and Ito stochastic Taylor expansions’, Math.Nachr. 151 (1991), 3350.
[3]Pandit, S.G. and Deo, S.G., Differential equations involving impulses, Lecture Notes in Mathematics 954 (Springer-Verlag, Berlin, Heidelberg, New York, 1982).
[4]Protter, M.H. and Morrey, C.B., A first course in real analysis (Springer-Verlag, Berlin, Heidelberg, New York, 1977).
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Taylor expansions for continuous Stieltjes differential equations

  • P.E. Kloeden (a1) and J. Panadiwal (a1)

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