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I am reading Section 3.3 of this paper, and trying to understand the proof of uniqueness of a global solution to the following equation defined on the Torus $\mathbb{T}^3$ \begin{align*} \mathrm{d} \...

Consider the Langevin equation ($N$-dimensional) with nonlinear drift term but expressible as a gradient of a function $U(\vec{x})$. Namely, consider the stochastic process described by the set of ...

I quote a paper from Delbaen and Shirakawa (2002). I will write in italics my observations/questions. Starting from a stochastic differential equation of the form: $$dr_t=\alpha\left(r_{\mu}-r_t\...