On Free Stochastic Differential Equations
Vladsislav Kargin
TL;DR
This paper derives a new equation for the Cauchy transform of solutions to free stochastic differential equations, enabling the analysis and solution of specific free SDE examples.
Contribution
It introduces a novel equation for the Cauchy transform in free SDEs, advancing the analytical tools available for free probability models.
Findings
Derived a new equation for the Cauchy transform of free SDE solutions
Solved several specific free SDE examples using the new equation
Enhanced understanding of free stochastic processes
Abstract
The paper derives an equation for the Cauchy transform of the solution of a free stochastic differential equation (SDE). This new equation is used to solve several particular examples of free SDEs.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and financial applications · Stochastic processes and statistical mechanics