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

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

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

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topEvans, 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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- [2] G. Barles, Thèse de 3e cycle, Univ. Paris IX, Dauphine, Paris, 1983.
- [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] 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] 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
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- [7] L.C. Evans, and H. Ishii, Differential games and nonlinear first-order PDE on bounded domains, to appear in Manuscripta Math. Zbl0559.35013MR767202
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- [9] W.H. Fleming, Inclusion probability and optimal stochastic control, IRIA Seminars Review, 1977. MR525182
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- [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] A. Friedman, Stochastic Differential Equations and Applications, Vol. II, Academic Press, New York, 1976. Zbl0323.60057
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- [14] P.L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Pitman, Boston, 1982. Zbl0497.35001MR667669
- [15] P.L. Lions, Existence results for first-order Hamilton-Jacobi equations, to appear. Zbl0552.70012MR740198
- [16] P.L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations I-III, to appear in Comm. PDE. Zbl0716.49023
- [17] P.E. Souganidis, Thesis, U. of Wisconsin, 1983.
- [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
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## Citations in EuDML Documents

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

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