Existence, uniqueness and ergodicity for the stochastic quantization equation

Studia Mathematica

Volumn 119, Issue 2, 1996, Pages 179-193

  Ga̧tarek, Dariusz ^a,b   GoŁdys, Beniamin ^b  

^a SYSTEMS RESEARCH INSTITUTE   (Poland)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Ergodicity; Nelson estimates; Stationary measure; Stochastic quantization; Wick powers

Indexed keywords

EID: 0040062332     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. [AR] S. Albeverio and M. Röckner, Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms, Probab. Theory Related Fields 89 (1991), 347-386.
2. [BCM] V. S. Borkar, R. T. Chari and S. K. Mitter, Stochastic quantization of field theory in finite and infinite volume, J. Funct. Anal. 81 (1988), 184-206.
3. [DZ] G. DaPrato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, 1992.
4. [H] R. Z. Hasminskii, Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, Aalpen an den Rijn, 1980.
5. 2 field, submitted.
6. [IW] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
7. [JM] G. Jona-Lasinio and P. K. Mitter, On the stochastic quantization of field theory, Comm. Math. Phys. 101 (1985), 409-436.
8. [LS] R. S. Liptser and A. N. Shiryaev, Statistics of Random Processes, Springer, New York, 1977.
9. [MT] S. P. Meyn and R. L. Tweedie, Stability of Markovian processes II: continuous-time processes and sampled chains, Adv. Appl. Probab. 25 (1993), 487-517.
10. [PW] G. Parisi and Y. S. Wu, Perturbation theory without gauge fixing, Sci. Sinica 24 (1981), 483-496.
11. 2 Euclidean (Quantum) Field Theory, Princeton University Press, Princeton, 1974.
12. [St] Ł. Stettner, Remarks on ergodic conditions for Markov processes on Polish spaces, Bull. Polish Acad. Sci. Math. 42 (1994), 103-114.
13. [W] L. Wu, Feynman-Kac semigroups, ground state diffusions and large deviations, J. Funct. Anal. 123 (1994), 202-231.