Abstract
In several contributions to this conference stochastic processes (especially those of diffusion type) have plaid a role. We would like to give a short exposition of some work done recently on the construction of such processes from a point of view which unifies the finite dimensional case (elliptic operators, heat equation, potential theory, quantum mechanics), the infinite dimensional case (variational equations, quantum fields) as well as the non commutative (finite or infinite dimensional) case (positive maps of C*-algebras, quantum statistical mechanics). The unification is achieved by the “method of Dirichlet forms” (or “energy forms”), which we shall now briefly expose, on the basis of the references [11 - [8], to which we refer for complements and bibliography.
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