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

  • Michael Röckner

Abstract

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]).

Keywords

Markov Process Dirichlet Form Free Field Martin Boundary Strong Markov Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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