×

zbMATH — the first resource for mathematics

Gaussian and non-Gaussian random fields associated with Markov processes. (English) Zbl 0533.60061
To every Markov process with a symmetric transition density, there correspond two random fields over the state space: a Gaussian field (the free field) \(\Phi\) and the occupation field T which describes the amount of time the particle spends at each state. The relation between the fields \(\Phi\) and T was established in the author’s paper, ibid. 50, 167- 187 (1983; Zbl 0522.60078), for the case of finite or countable index space. It is extended to the general case which covers, in particular, the fields associated with the Brownian motion.
Reviewer: Y.Asoo

MSC:
60G60 Random fields
81P20 Stochastic mechanics (including stochastic electrodynamics)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Brydges, D; Fröhlich, J; Spencer, T, The random walk representation of classical spin systems and correlation inequalities, Comm. math. phys., 83, 123-150, (1982)
[2] Dynkin, E.B, Theory of Markov processes, (1960), Pergamon Oxford · Zbl 0096.11704
[3] Dynkin, E.B, Regular Markov processes, (), 187-218 · Zbl 0522.60078
[4] Dynkin, E.B, Markov representations of stochastic systems, (), 219-258 · Zbl 0323.60070
[5] Dynkin, E.B, Additive functionals of several time-reversible Markov processes, J. funct. anal., 42, 64-101, (1981) · Zbl 0467.60069
[6] Dynkin, E.B, Green’s and Dirichlet spaces associated with fine Markov processes, J. funct. anal., 47, 381-418, (1982) · Zbl 0488.60083
[7] Dynkin, E.B, Markov processes as a tool in field theory, J. funct. anal., 50, 167-187, (1983) · Zbl 0522.60078
[8] Dynkin, E.B, Local times and quantum fields, () · Zbl 0554.60058
[9] Feller, W, ()
[10] Meyer, P.A, Probability and potential, (1966), Blaisdell Waltham, Mass./Toronto/London
[11] Simon, B, The P(φ)2 Euclidean (quantum) field theory, ()
[12] Symanzik, K, Euclidean quantum field theory, () · Zbl 0195.55902
[13] Wolpert, R.L, Local time and a particle picture for Euclidean field theory, J. funct. anal., 30, 341-357, (1978) · Zbl 0464.70016
[14] Yang, W.S, Correlation inequalities of lattice φ4 interactions, (1983), Cornell Univ Ithaca, preprint
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.