Journal of Theoretical Probability

, Volume 29, Issue 4, pp 1444–1457 | Cite as

Picard Iterations for Diffusions on Symmetric Matrices

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Abstract

Matrix-valued stochastic processes have been of significant importance in areas such as physics, engineering and mathematical finance. One of the first models studied has been the so-called Wishart process, which is described as the solution of a stochastic differential equation in the space of matrices. In this paper, we analyze natural extensions of this model and prove the existence and uniqueness of the solution. We do this by carrying out a Picard iteration technique in the space of symmetric matrices. This approach takes into account the operator character of the matrices, which helps to corroborate how the Lipchitz conditions also arise naturally in this context.

Keywords

Matrix-valued diffusions Lipschitz conditions Picard iterations 

Mathematics Subject Classification (2010)

60J60 58J65 
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Notes

Acknowledgments

We thank the hospitality of Piotr Graczyk in Université d’Anger where this project was started. We also thank the anonymous referee for all the help to improve this paper.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Departamento de MatematicasCINVESTAV-IPNMexicoMexico

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