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dc.contributor.advisorLyons, J. T.
dc.contributor.authorSipiläinen, Eeva-Maria
dc.date.accessioned2013-11-27T10:25:21Z
dc.date.available2013-11-27T10:25:21Z
dc.date.issued1993
dc.identifier.urihttp://hdl.handle.net/1842/8202
dc.description.abstractThe Ito-Stratonovich theory of stochastic integration and stochastic differential equations has several shortcomings, especially when it comes to existence and consistency with the theory of Lebesque-Stieltjes integration and ordinary differential equations. An attempt is made firstly, to isolate the path property, possessed by almost all Brownian paths, that makes the stochastic theory of integration work. Secondly, to construct a new concept of solutions for differential equations, which would have the required consistency and continuity properties, within a class of deterministic noise functions, large enough to include almost all Brownian paths. The algebraic structure of iterated path integrals for smooth paths leads to a formal definition of a solution for a differential equation in terms of generalized path integrals for more general noises. This suggests a way of constructing solutions to differential equations in a large class of paths as limits of operators. The concept of the driving noise is extended to include the generalized path integrals of the noise. Less stringent conditions on the Holder continuity of the path can be compensated by giving more of its iterated integrals. Sufficient conditions for the solution to exist are proved in some special cases, and it is proved that almost all paths of Brownian motion as well as some other stochastic processes can be included in the theory.en_US
dc.contributor.sponsorAcademy of Finlanden_US
dc.contributor.sponsorBritish Councilen_US
dc.contributor.sponsorSuomen Kulttuurirahastoen_US
dc.contributor.sponsorSuomalainen Konkordialiittoen_US
dc.language.isoenen_US
dc.publisherThe University of Edinburghen_US
dc.subjectStochastic integral equationsen_US
dc.subjectStochastic differential equationsen_US
dc.titlePathwise view on solutions of stochastic differential equationsen_US
dc.typeThesis or Dissertationen_US
dc.type.qualificationlevelDoctoralen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US


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