Phase II: ergodicity for singular stochastic equations

Period: 01.01.2021-31.12.2021.

Activity. The research conducted during the second phase of this project has two parts. In the first one we continued the work initiated in the first phase, regarding I.i) the contruction of path-continuous Markov processes, I.ii) the numerical reconstruction of solutions for inverse Cauchy problems and I.iii) the construction of Hunt processes by means of Lyapunov functions. The second part was mainly devoted to II.i) the study of ergodicity for Markov processes, in particular for singular SDEs in Hilbert spaces; but also to II.ii) the problem of driving a Markov process by a stochastic or deterministic flow in the spirit of parallel transport.

Detailed report of Phase II (in Romanian):