Feynman Graph Representation to Stochastic Differential Equations Driven by Lévy Noise

Boubaker Smii ()
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Boubaker Smii: King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics

A chapter in International Conference on Mathematical Sciences and Statistics 2013, 2014, pp 213-222 from Springer

Abstract: Abstract Stochastic differential equations driven by Lévy noise are intensively studied. But so far there seems to be no recipe to find out what kind of noise it is, given the general structure of the equation. This can be obtained by recalling a graphical representation of the solution of the stochastic differential equations driven by Lévy noise. The graphs introduced are called generalized Feynman graphs and a numerical value will be assigned to each graph. Our graphs’ formalism can be applied to different kinds of stochastic differential equations. As an example, a graphical representation of the generalized Ornstein–Uhlenbeck process will be given in this work.

Keywords: Graphical Representation; Stochastic Differential Equation; Rooted Tree; Feynman Graph; Stochastic Partial Differential Equation (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-4585-33-0_22

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DOI: 10.1007/978-981-4585-33-0_22

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