Fractional derivatives, non-symmetric and time-dependent Dirichlet forms and the drift form (Q5926116)

By using fractional derivatives, the authors show that the bilinear form induced by any Lévy process is the limit of some non-symmetric Dirichlet forms. In particular, the drift form \(\int^{\infty}_{-\infty}u(x)\frac{dv(x)}{dx} dx\) is the limit of some non-symmetric Dirichlet forms. For drift forms in \(\mathbb{R}^n\) with variable coefficients, a similar result is true if the coefficients satisfy some regularity and commutator conditions. The authors also show that time-dependent Dirichlet forms can also be realized as limits of ordinary non-symmetric Dirichlet forms.