EXPLICIT STRONG SOLUTIONS OF MULTIDIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS

Michael A. Kouritzin () and Bruno Remillard ()
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Michael A. Kouritzin: Department of Mathematical and Statistical Sciences, University of Alberta

No lrsp-TRS368, RePAd Working Paper Series from Département des sciences administratives, UQO

Abstract: Herein, we characterize strong solutions of multidimensional stochastic differential equations (formula) that can be represented locally as (formula) where W is an multidimensional Brownian motion and U, (symbole) are continuous functions. Assuming that (symbole) is continuously differentiable, we find that (symbole) must satisfy a commutation relation for such explicit solutions to exist and we identify all drift terms b as well as U and (symbole) that will allow X to be represented in this manner. Our method is based on the existence of a local change of coordinates in terms of a diffeomorphism between the solutions X and the strong solutions to a simpler Ito integral equation.

Keywords: Diffeomorphism; Ito processes; explicit solutions. (search for similar items in EconPapers)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Date: Written 2000-01-01
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