On solutions of stochastic differential equations with parameters modeled by random sets

Authors:
Bernhard Schmelzer
Affiliations:
Universität Innsbruck, Institut für Grundlagen der Bauingenieurwissenschaften, AB Technische Mathematik, A-6020 Innsbruck, Austria
Venue:
International Journal of Approximate Reasoning
Year:
2010

Citing 3
Cited 1

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Classical and imprecise probability methods for sensitivity analysis in engineering: A case study

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Stochastic differential equations with fuzzy drift and diffusion

Fuzzy Sets and Systems

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Abstract

We consider ordinary stochastic differential equations whose coefficients depend on parameters. After giving conditions under which the solution processes continuously depend on the parameters random compact sets are used to model the parameter uncertainty. This leads to continuous set-valued stochastic processes whose properties are investigated. Furthermore, we define analogues of first entrance times for set-valued processes called first entrance and inclusion times. The theoretical concept is applied to a simple example from mechanics.