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## Drifting Markov processes via generalized linear models

Drifting Markov processes via generalized linear models

Salle des séminaires M.0.1

LMRS

In this presentation, firstly, the limitations of linear models under the assumption of support point matrices in the sequence of transition matrices are discussed and the results corresponding to suitable basis functions under this assumption are presented (polynomial basis functions – considered in [Vergne2008], but not optimized under stochasticity constraints – and finite element basis functions). Secondly, extensions of this model are introduced, by dropping the assumption of support point matrices in the sequence of the transition matrices, and considering finite support probability mass functions as basis functions. Then, by dropping the stochasticity assumption for the support point matrices (hence free parameters) and considering a generalized linear model assuring the stochasticity via a softmax link function – corresponding to a logistic model.