A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities

L. C. Evans; H. Ishii

Annales de l'I.H.P. Analyse non linéaire (1985)

  • Volume: 2, Issue: 1, page 1-20
  • ISSN: 0294-1449

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Evans, L. C., and Ishii, H.. "A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities." Annales de l'I.H.P. Analyse non linéaire 2.1 (1985): 1-20. <http://eudml.org/doc/78086>.

@article{Evans1985,
author = {Evans, L. C., Ishii, H.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {viscosity solution methods for Hamilton-Jacobi PDE; WKB-type representations},
language = {eng},
number = {1},
pages = {1-20},
publisher = {Gauthier-Villars},
title = {A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities},
url = {http://eudml.org/doc/78086},
volume = {2},
year = {1985},
}

TY - JOUR
AU - Evans, L. C.
AU - Ishii, H.
TI - A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1985
PB - Gauthier-Villars
VL - 2
IS - 1
SP - 1
EP - 20
LA - eng
KW - viscosity solution methods for Hamilton-Jacobi PDE; WKB-type representations
UR - http://eudml.org/doc/78086
ER -

References

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  1. [1] D.G. Aronson, The fundamental solution of a linear parabolic equation containing a small parameter, Ill. J. Math., t. 3, 1959, p. 580-619. Zbl0090.07601MR107758
  2. [2] G. Barles, Thèse de 3e cycle, Univ. Paris IX, Dauphine, Paris, 1983. 
  3. [3] E.N. Barron, L.C. Evans, and R. Jensen, Viscosity solutions of Isaacs' equations and differential games with Lipschitz controls, to appear in J. Diff. Eq. Zbl0548.90104
  4. [4] I. Capuzzo Dolcetta and L.C. Evans, Optimal switching for ordinary differential equations, to appear in SIAM J. Control and Op., t. 22, 1984, p. 143- 161. Zbl0641.49017MR728678
  5. [5] M.G. Grandall, L.C. Evans, and P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. AMS., t. 282, 1984, p. 487-502. Zbl0543.35011MR732102
  6. [6] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. AMS, t. 277, 1983, p. 1-42. Zbl0599.35024MR690039
  7. [7] L.C. Evans, and H. Ishii, Differential games and nonlinear first-order PDE on bounded domains, to appear in Manuscripta Math. Zbl0559.35013MR767202
  8. [8] L.C. Evans and P.E. Souganidis, Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations, to appear in Indiana U. Math. J. Zbl1169.91317MR756158
  9. [9] W.H. Fleming, Inclusion probability and optimal stochastic control, IRIA Seminars Review, 1977. MR525182
  10. [10] W.H. Fleming, Exit probabilities and optimal stochastic control, Appl. Math. Op., t. 4, 1978, p. 329-346. Zbl0398.93068MR512217
  11. [11] W.H. Fleming, Logarithmic transformations and stochastic control, in Advances in Filtering and Stochastic Control (ed. by Fleming and Gorostiza), Springer, New York, 1983. Zbl0502.93076MR794510
  12. [12] A. Friedman, Stochastic Differential Equations and Applications, Vol. II, Academic Press, New York, 1976. Zbl0323.60057
  13. [13] C.J. Holland, A minimum principle for the principal eigenvalue of second order linear elliptic equations with natural boundary conditions, Comm. Pure Appl. Math., t. 31, 1978, p. 509-519. Zbl0388.35053MR466940
  14. [14] P.L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, 1982. Zbl0497.35001MR667669
  15. [15] P.L. Lions, Existence results for first-order Hamilton-Jacobi equations, to appear. Zbl0552.70012MR740198
  16. [16] P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations I-III, to appear in Comm. PDE. Zbl0716.49023
  17. [17] P.E. Souganidis, Thesis, U. of Wisconsin, 1983. 
  18. [18] S.R.S. Varadhan, On the behavior of the fundamental solution of the heat equation with variable coefficients, Comm. Pure Appl. Math., t. 20, 1967, p. 431-455. Zbl0155.16503MR208191
  19. [19] A.D. Ventcel and M.I. Freidlin, On small random perturbations of dynamical systems, Russian Math. Surveys, t. 25, 1970, p. 1-56. Zbl0297.34053MR267221

Citations in EuDML Documents

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  1. L. C. Evans, P. E. Souganidis, G. Fournier, M. Willem, A PDE approach to certain large deviation problems for systems of parabolic equations
  2. A. Piatnitski, A. Rybalko, V. Rybalko, Ground states of singularly perturbed convection-diffusion equation with oscillating coefficients
  3. G. Barles, L. Bronsard, P. E. Souganidis, Front propagation for reaction-diffusion equations of bistable type
  4. Magdalena Kobylanski, Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections
  5. Brett Kotschwar, Lei Ni, Local gradient estimates of p -harmonic functions, 1 / H -flow, and an entropy formula
  6. Martino Bardi, An asymptotic formula for the Green's function of an elliptic operator
  7. Wendell H. Fleming, Panagiotis E. Souganidis, PDE-viscosity solution approach to some problems of large deviations
  8. Italo Capuzzo Dolcetta, Soluzioni di viscosità

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