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math.PR2018
Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients
Rengming Song, Longjie Xie
Consider the following time-dependent stable-like operator with drift $$ \mathscr{L}_tφ(x)=\int_{\mathbb{R}^d}\big[φ(x+z)-φ(x)-z^{(α)}\cdot\nablaφ(x)\big]σ(t,x,z)ν_α(d z)+b(t,x)\cd…
math.PR2018★ 1 cited
Well-posedness and long time behavior of singular Langevin stochastic differential equations
Renming Song, Longjie Xie
In this paper, we study damped Langevin stochastic differential equations with singular velocity fields. We prove the strong well-posedness of such equations. Moreover, by combinin…