Claude Dellacherie

Description of the sub-Markov kernel associated to generalized ultrametric matrices. An algorithmic approach

Abstract We supply a simple algorithm which describes the sub-Markov kernel P associated to a nonsingular generalized ultrametric matrix U. This algorithm is based on the dyadic tree structure of U, it identifies the exiting roots of P and P t , and the couples i≠j for which P ij >0 (equivalently (U −1 ) ij ).

Inverse M-matrices and ultrametric matrices

Inverse M - matrices and potentials.- Ultrametric Matrices.- Graph of Ultrametric Type Matrices.- Filtered Matrices.- Hadamard Functions of Inverse M - matrices.- Notes and Comments Beyond Matrices.- Basic Matrix Block Formulae.- Symbolic Inversion of a Diagonally Dominant M - matrices.- Bibliography.- Index of Notations.- Index.

Hadamard Functions of Inverse

We prove that the class of generalized ultrametric matrices (GUM) is the largest class of bipotential matrices stable under Hadamard increasing functions. We also show that any power

M

\alpha\ge1

-Matrices

, in the sense of Hadamard functions, of an inverse

Noyaux potentiels associés à une filtration

M

Autour des Ensembles Semi-Polaires

-matrix is also inverse

Nonlinear Dirichlet Problem and Nonlinear Integration

M

The Class of Inverse

-matrix. This was conjectured for

M

\alpha=2