Stochastic differential equations for Dirichlet processes

By Richard F. Bass, Zhen-Qing Chens. 2001

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One-Dimensional Stochastic Differential Equations with Singular and Degenerate Coefficients (2005, result): “These results extend early work on strong solutions and pathwise uniqueness for one-dimensional SDEs, such as that in Yamada-Watanabe [15], Nakao [13], Le Gall [11]-[12], and Barlow-Perkins [2], as well as later work by Zhang [16] and by Bass-Chen [ 4 ].”
Rough paths and 1d SDE with a time dependent distributional drift: application to polymers (2014, background): “In this setting, unique solvability can be proved to hold in the weak or strong sense according to the regularity of Y , see for example the papers by Flandoli, Russo and Wolf [12, 13] on the one hand and the paper by Bass and Chen [3] on the other hand.”
On the constructions of the skew Brownian motion (2007, background): “In addition, some Dirichlet processes can be constructed as solutions of equations of this type [8, 25].”
Some parabolic PDEs whose drift is an irregular random noise in space (2006, background): “Bass and Chen [2] were also interested in (1.4) and provided a well-stated framework when σ is 12 -Hölder continuous and b is γ -Hölder continuous, γ > 1 2 .”