On the Markov property of strong solutions to SDE with generalized coefficients
Ludmila L. Zaitseva
TL;DR
This paper proves that strong solutions to certain multidimensional stochastic differential equations with coefficients involving local time on a hyperplane possess the Markov property, providing a complete proof for this class of SDEs.
Contribution
It offers a complete proof of the Markov property for strong solutions to multidimensional SDEs with coefficients involving local time on a hyperplane.
Findings
Established the Markov property for solutions with local time coefficients
Extended understanding of SDEs with boundary interactions
Provided rigorous proof for a class of multidimensional SDEs
Abstract
We show the complete proof of the Markov property of the strong solution to a multidimensional SDE whose coefficients involve local time on a hyperplane of the unknown process.
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Taxonomy
TopicsStochastic processes and financial applications · Stability and Controllability of Differential Equations · Mathematical Dynamics and Fractals