The notion of stochastic lexicalized tree-adjoining grammar (SLTAG) is formally defined. The parameters of a SLTAG correspond to the probability of combining two structures each one associated with a word. The characteristics of SLTAG are unique and novel since it is lexieally sensitive (as N-gram models or Hidden Markov Models) and yet hierarchical (as stochastic context-free grammars).Then, two basic algorithms for SLTAG arc introduced: an algorithm for computing the probability of a sentence generated by a SLTAG and an inside-outside-like iterative algorithm for estimating the parameters of a SLTAG given a training corpus.Finally, we should how SLTAG enables to define a lexicalized version of stochastic context-free grammars and we report preliminary experiments showing some of the advantages of SLTAG over stochastic context-free grammars.