A simple stochastic approach, designed to model the movement of electrons throughout chemical bonds, is introduced. This model makes use of a Markov matrix to codify useful structural information in QSAR. The self-return probabilities of this matrix throughout time ((SR)pi(k)) are then used as molecular descriptors. Firstly, a calculation of (SR)pi(k) is made for a large series of anticancer and non-anticancer chemicals. Then, k-Means Cluster Analysis allows us to split the data series into clusters and ensure a representative design of training and predicting series. Next, we develop a classification function through Linear Discriminant Analysis (LDA). This QSAR discriminates between anticancer compounds and non-active compounds with a correct global classification of 90.5% in the training series. The model also correctly classified 86.07% of the compounds in the predicting series. This classification function is then used to perform a virtual screening of a combinatorial library of coumarins. In this connection, the biological assay of some furocoumarins, selected by virtual screening using the present model, gives good results. In particular, a tetracyclic derivative of 5-methoxypsoralen (5-MOP) has an IC50 against HL-60 tumoral line around 6 to 10 times lower than those for 8-MOP and 5-MOP (reference drugs), respectively. Finally, application of Iso-contribution Zone Analysis (IZA) provides structural interpretation of the biological activity predicted with this QSAR.