A PDE approach to certain large deviation problems for systems of parabolic equations

L. C. Evans; P. E. Souganidis; G. Fournier; M. Willem

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: S6, page 229-258
  • ISSN: 0294-1449

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Evans, L. C., et al. "A PDE approach to certain large deviation problems for systems of parabolic equations." Annales de l'I.H.P. Analyse non linéaire S6 (1989): 229-258. <http://eudml.org/doc/78197>.

@article{Evans1989,
author = {Evans, L. C., Souganidis, P. E., Fournier, G., Willem, M.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {parabolic equation; Hamilton-Jacobi equation; exponential decay properties; large deviations techniques},
language = {eng},
pages = {229-258},
publisher = {Gauthier-Villars},
title = {A PDE approach to certain large deviation problems for systems of parabolic equations},
url = {http://eudml.org/doc/78197},
volume = {S6},
year = {1989},
}

TY - JOUR
AU - Evans, L. C.
AU - Souganidis, P. E.
AU - Fournier, G.
AU - Willem, M.
TI - A PDE approach to certain large deviation problems for systems of parabolic equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - S6
SP - 229
EP - 258
LA - eng
KW - parabolic equation; Hamilton-Jacobi equation; exponential decay properties; large deviations techniques
UR - http://eudml.org/doc/78197
ER -

References

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  2. 2. M.G. Crandall, L.C. Evans, and P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. AMS82 (1984), 487-502. Zbl0543.35011MR732102
  3. 3. M.G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. AMS277 (1983), 1-42. Zbl0599.35024MR690039
  4. 4. M.D. Donsker and S.R.S. Varadhan, On a variational formula for the principal eigenvalue for operators with a maximum principle, Proc. Nat. Acad. Sci. USA72 (1975), 780-783. Zbl0353.49039MR361998
  5. 5. R. Ellis, Entropy, Large Deviations and Statistical Mechanisms, Springer, New York, 1985. Zbl0566.60097MR793553
  6. 6. L.C. Evans and H. Ishii, A PDE approach to some asymptotic problems concerning random differential equation with small noise intensities, Ann. L'Institut H. Poincaré2 (1985), 1-20. Zbl0601.60076MR781589
  7. 7. L.C. Evans and P.E. Souganidis, Differential games and representation formulas for solutions of Hamilton-Jacobi equations, Indiana U. Math. J.33 (1984), 773-797. Zbl1169.91317MR756158
  8. 8. L.C. Evans and P.E. Souganidis, A PDE approach to geometric optics for certain semilinear parabolic equations, to appear. Zbl0692.35014MR982575
  9. 9. W. Fleming and P.E. Souganidis, A PDE approach to asymptotic estimates for optional exit probabilities, Annali Scuola Norm. Sup. Pisa. Zbl0576.93067
  10. 10. M.I. Freidlin and A.D. Wentzell, Random Perturbations of Dynamical Systems, Springer, New York, 1984. Zbl0522.60055MR722136
  11. 11. F.R. Gantmacher, The Theory of Matrices (Vol. II), Chelsea, New York, 1959. Zbl0085.01001
  12. 12. S. Karlin and H.M. Taylor, A First Course in Stochastic Processes (2nd ed.), Academic Press, New York, 1975. Zbl0315.60016MR356197
  13. 13. S. Koike, An asymptotic formula for solutions of Hamilton-Jacobi-Bellman equations, preprint. Zbl0623.49016MR881728
  14. 14. P.E. Souganidis, Existence of viscosity solutions of Hamilton-Jacobi equations, J. Diff. Eq.56 (1985), 345-390. Zbl0506.35020MR780496

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