Fast oscillating random perturbations of dynamical systems with conservation laws

A. N. Borodin; M. I. Freidlin

Annales de l'I.H.P. Probabilités et statistiques (1995)

  • Volume: 31, Issue: 3, page 485-525
  • ISSN: 0246-0203

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Borodin, A. N., and Freidlin, M. I.. "Fast oscillating random perturbations of dynamical systems with conservation laws." Annales de l'I.H.P. Probabilités et statistiques 31.3 (1995): 485-525. <http://eudml.org/doc/77519>.

@article{Borodin1995,
author = {Borodin, A. N., Freidlin, M. I.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random perturbations; conservation laws; stochastic dynamical systems; averaging principle},
language = {eng},
number = {3},
pages = {485-525},
publisher = {Gauthier-Villars},
title = {Fast oscillating random perturbations of dynamical systems with conservation laws},
url = {http://eudml.org/doc/77519},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Borodin, A. N.
AU - Freidlin, M. I.
TI - Fast oscillating random perturbations of dynamical systems with conservation laws
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1995
PB - Gauthier-Villars
VL - 31
IS - 3
SP - 485
EP - 525
LA - eng
KW - random perturbations; conservation laws; stochastic dynamical systems; averaging principle
UR - http://eudml.org/doc/77519
ER -

References

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  1. [1] A.N. Borodin, Limit theorem for solutions of differential equations with random right-hand side, Theory Prob. Appl., Vol. 22, 3, 1977, pp. 482-497. Zbl0412.60067MR517995
  2. [2] R. Cogburn and J.A. Ellison, A stochastic theory of adiabatic invariance, Comm. Math. Phys., Vol. 149, 1992, pp. 97-126. Zbl0755.60095MR1182412
  3. [3] J.L. Doob, Stochastic Processes, Wiley, New York, 1960. Zbl0053.26802MR58896
  4. [4] M.I. Freidlin, Functional Integration and Partial Differential Equations, Princeton Univ. Press., 1985. Zbl0568.60057MR833742
  5. [5] M.I. Freidlin and A.D. Wentzell, Random Perturbations of Dynamical Systems, Springer-Verlag, 1984. Zbl0522.60055MR722136
  6. [6] M.I. Freidlin and A.D. Wentzell, Diffusion process on graphs and averaging principle, The Annals of Probability, Vol. 21, 4, 1993, pp. 2215-2245. Zbl0795.60042MR1245308
  7. [7] M.I. Freidlin and A.D. Wentzell, Random perturbation of Hamiltonian Systems, to appear in The Memoirs AMS. Zbl0804.60070MR1201269
  8. [8] R.Z. Khasminskii, A limit thorem for solutions of differential equations with random right-hand side, Theory Prob. Appl., Vol. 11, 3, 1966, pp. 390-406. Zbl0202.48601
  9. [9] R.Z. Khasminskii, On processes defined by differential equations with a small parameter, Theory Prob. Appl., Vol. 11, 2, 1966, pp. 211-228. Zbl0168.16002
  10. [10] I.A. Ibragimov and Yu.A. Rozanov, Gaussian Randum Processes, Springer-Verlag, 1978. Zbl0392.60037
  11. [11] Yu V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Prob. Appl., Vol. 1, 2, 1956, pp. 157-214. Zbl0075.29001
  12. [12] A.D. Wentzell, A course in the theory of stochastic processes, McGraw-Hill Inc., 1981. Zbl0502.60001

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