We define a class of not necessarily linear C0-semigroups (Pt)t≥0 on Cb(E) (more generally, on Cκ(E):=1κCb(E), for some growth bounding continuous function κ) equipped with the mixed topology τM1 for a large class of topological state spaces E. In the linear case we prove that such...

We define a class of not necessarily linear C0-semigroups (Pt)t≥0 on Cb(E) (more generally, on Cκ(E):=1κCb(E), for some growth bounding continuous function κ) equipped with the mixed topology τM1 for a large class of topological state spaces E. In the linear case we prove that such...

This article focuses on a new concept of quadratic variation for processes taking values in a Banach space B and a corresponding covariation. This is more general than the classical one of Métivier and Pellaumail. Those notions are associated with some subspace ? of the dual of the projective...

We give a direct proof of the Harnack inequality for a class of Kolmogorov operators associated with a linear SDE and we find the explicit expression of the optimal Harnack constant. We discuss some possible implication of the Harnack inequality in finance: specifically we infer no-arbitrage...

The method of evaluation of stochastic volatility (SV) model coefficients, with time going to the infinity, is consid-ered. The problem of finding the solution of a system of stochastic differential equations is reduced to that of the analytical solution of the Fokker-Planck-Kolmogorov...

The method of evaluation of stochastic volatility (SV) model coefficients, with time approaching the infinity, is consid-ered. The problem of finding the solution of a system of stochastic differential equations is reduced to that of the ana-lytical solution of the Fokker–Planck–Kholmogorov...