On the Transition Function of the Infinite Dimensional Ornstein-Uhlenbeck Process Given by the Free Quantum Field

  • Michael Röckner


In this paper we want to investigate a particular semigroup (πt)t>0 of probability kernels defined on some infinite dimensional Banach space Bα contained in Y’(ℝd−1) (i.e. the tempered distributions on ℝd-1), d ≥ 2,
$$\alpha \in ]\frac{{d - 2}}{2},\infty$$
. This semigroup (πt)t>0 is the transition function of the infinite dimensional Ornstein-Uhlenbeck process given by the free field of Euclidean quantum field theory on ℝd (cf. [1], [2]). We will establish that (πt)t>0 has the Feller property, determine its generator (on a suitable domain) and its Dirichlet form. Furthermore, we will characterise the associated entrance space in the sense of Dynkin (cf. [3], [4], [5]).


Markov Process Dirichlet Form Free Field Martin Boundary Strong Markov Property 
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Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Michael Röckner
    • 1
  1. 1.Department of MathematicsUniversity of EdinburghEdinburghScotland

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