International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

Rajter-Ćirić D.   Selesi D.  

Nonlinear stochastic differential equations containing generalized delta processes

Reporter: Rajter-Ćirić D.

Some classes of nonlinear stochastic differential equations involving the generalized delta process and its derivatives are considered in the framework of the Colombeau generalized stochastic process theory. All initial problems considered are proven to have a unique unbiased solution. Several examples are exposed that provide more insight into the assumptions made in the theorems. The paper involves new results on stochastic nonlinear models with singularities, and both the Colombeau algebra approach and the chaos expansion method open the door also to future numerical approximations.

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