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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4265

Title: An analytical introduction to stochastic differential equations: Part I - the Langevin equation
Authors: Clément, Ph.
van Gaans, O. W.
Issue Date: 2000
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Citation: Ph. Clément and O. W. van Gaans, "An analytical introduction to stochastic differential equations: Part I - the Langevin equation", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2000), pp. 217-269.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 (2000)
Abstract: We present an introduction to the theory of stochastic differential equations, motivating and explaining ideas from the point of view of analysis. First the notion of white noise is developed, introducing at the same time probabilistic tools. Then the one dimensional Langevin equation is formulated as a deterministic integral equation with a parameter. Its solution leads to stochastic convolution, which is defined as a Riemann-Stieltjes integral. It is shown that the parameter dependence yields a Gaussian system, of which the means and covariances arde computed. We conclude by introducing briefly the notion of invariant measure and the associated Kolmogorov equations.
URI: http://hdl.handle.net/10077/4265
ISSN: 0049-4704
Appears in Collections:Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.32 (2000)

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