Existence, uniqueness and ergodicity for the stochastic quantization equation

Dariusz Gątarek; Beniamin Gołdys

Studia Mathematica (1996)

  • Volume: 119, Issue: 2, page 179-193
  • ISSN: 0039-3223

Abstract

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Existence, uniqueness and ergodicity of weak solutions to the equation of stochastic quantization in finite volume is obtained as a simple consequence of the Girsanov theorem.

How to cite

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Gątarek, Dariusz, and Gołdys, Beniamin. "Existence, uniqueness and ergodicity for the stochastic quantization equation." Studia Mathematica 119.2 (1996): 179-193. <http://eudml.org/doc/216293>.

@article{Gątarek1996,
abstract = {Existence, uniqueness and ergodicity of weak solutions to the equation of stochastic quantization in finite volume is obtained as a simple consequence of the Girsanov theorem.},
author = {Gątarek, Dariusz, Gołdys, Beniamin},
journal = {Studia Mathematica},
keywords = {Wick powers; Nelson estimates; stochastic quantization; stationary measure; ergodicity; uniqueness and ergodicity of weak solutions; Girsanov theorem},
language = {eng},
number = {2},
pages = {179-193},
title = {Existence, uniqueness and ergodicity for the stochastic quantization equation},
url = {http://eudml.org/doc/216293},
volume = {119},
year = {1996},
}

TY - JOUR
AU - Gątarek, Dariusz
AU - Gołdys, Beniamin
TI - Existence, uniqueness and ergodicity for the stochastic quantization equation
JO - Studia Mathematica
PY - 1996
VL - 119
IS - 2
SP - 179
EP - 193
AB - Existence, uniqueness and ergodicity of weak solutions to the equation of stochastic quantization in finite volume is obtained as a simple consequence of the Girsanov theorem.
LA - eng
KW - Wick powers; Nelson estimates; stochastic quantization; stationary measure; ergodicity; uniqueness and ergodicity of weak solutions; Girsanov theorem
UR - http://eudml.org/doc/216293
ER -

References

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  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. Zbl0725.60055
  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. Zbl0657.60084
  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. [HK] Y. Z. Hu and G. Kallianpur, Singular infinite-dimensional SDE and stochastic quantization of P ( ϕ ) 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. Zbl0588.60054
  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. Zbl0781.60052
  10. [PW] G. Parisi and Y. S. Wu, Perturbation theory without gauge fixing, Sci. Sinica 24 (1981), 483-496. 
  11. [Si] B. Simon, The P ( ϕ ) 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. Zbl0815.60072
  13. [W] L. Wu, Feynman-Kac semigroups, ground state diffusions and large deviations, J. Funct. Anal. 123 (1994), 202-231. Zbl0798.60067

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