Regularization by noise and approximations of singular kinetic SDEs

Regularisation by noise in the context of stochastic differential equations (SDEs) with coefficients of low regularity, known as singular SDEs, refers to the beneficial effect produced by noise so that the singularity from the coefficients is smoothed out yielding well-behaved equations. Kinetic SDEs, also sometimes called second order SDEs, as one typical type of stochastic Hamiltonian systems, describe the motion of a particle perturbed by some random external force. The difference of comparing it with usual SDEs is that the noise of the space position vanishes and only appears in the direction of velocity, hence less noise gets involved in the system. In this talk we will discuss about the regularization effect by the degenerate noise for the singular kinetic SDEs from numerical approximation and also particles approximation view point.