Let\(\varSigma \)be a finite non-empty alphabet of symbols. Then\(\varSigma ^*\)denotes the set of strings over the alphabet\(\varSigma \)including the empty string\(\varepsilon \). The length of a stringwis denoted by |w|, and the number of occurrences of a symbolain a stringw...
\begin{aligned} dX_t = b(X_{t-}) \, dt + \sigma (X_{t-}) \, dL_t, \qquad X_0 = x. \end{aligned} (7.8) The solution does not explode in finite time and gives rise to a Markovian {\mathcal {C}}_\infty -Feller semigroup with symbol \begin{aligned} q(x,\xi )...
whereMis a compactn-dimensional Riemannian manifold andFrom the presence of the two parametersA,B, it is not straightforward which is the notion of best constants in this case. The issue of defining and determining the best constants in () has been the central role of the celebratedAB-program...