Besov regularity for the generalized local time of the indefinite Skorohod integral
Consider a process given as an indefinite Skorokhod integral \(X_t=\int_0^tu_s\,dW_s\). In an article by \textit{C. A. Tudor} [Bernoulli 10, No. 2, 313--325 (2004; Zbl 1062.60055)], it has been proved that this process can also be written as \(X_t=\int_0^tE[v_s| F_{[s,t]^c}]\,dW_s\), where \(v\) is a process which can be deduced from \(u\) by means of Malliavin's calculus. As an application, it is possible to construct a generalized local time \(L_t^X(x)\). The aim of the article under review is to study the Besov regularity of \(x\mapsto L_t^X(x)\); it appears to be similar to the regularity of the Brownian motion \(t\mapsto W_t\).
scientific article; zbMATH DE number 5128138