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On noncooperative $n$-player principal eigenvalue games
1. | Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, United States, United States |
References:
[1] |
J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 1984. |
[2] |
G. K. Befekadu, V. Gupta and P. J. Antsaklis, Characterization of feedback Nash equilibria for multi-channel systems via a set of non-fragile stabilizing state-feedback solutions and dissipativity inequalities, J. Math. Contr. Sign. Syst., 25 (2013), 311-326.
doi: 10.1007/s00498-012-0105-z. |
[3] |
M. V. Day, On the exponential exit law in the small parameter exit problem, Stochastics, 8 (1983), 297-323.
doi: 10.1080/17442508308833244. |
[4] |
M. V. Day, Recent progress on the small parameter exit problem, Stochastics, 20 (1987), 121-150.
doi: 10.1080/17442508708833440. |
[5] |
M. V. Day and T. A. Darden, Some regularity results on the Ventcel-Freidlin quasipotential function, Appl. Math. Optim., 13 (1985), 259-282.
doi: 10.1007/BF01442211. |
[6] |
A. Devinatz and A. Friedman, Asymptotic behavior of the principal eigenfunction for a singularly perturbed Dirichlet problem, J. Indiana Univ. Math., 27 (1978), 143-157.
doi: 10.1512/iumj.1978.27.27012. |
[7] |
A. Friedman, Stochastic Differential Equations and Applications, Vol. 2, Academic Press, 1976. |
[8] |
I. L. Glicksberg, A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc., 3 (1952), 170-174. |
[9] |
Y. Kifer, On the principal eigenvalue in a singular perturbation problem with hyperbolic limit points and circles, J. Diff. Equ., 37 (1980), 108-139.
doi: 10.1016/0022-0396(80)90092-3. |
[10] |
Y. Kifer, The inverse problem for small random perturbations of dynamical systems, Israel J. Math., 40 (1981), 165-174.
doi: 10.1007/BF02761907. |
[11] |
S. J. Sheu, Some estimates of the transition density of a non-degenerate diffusion Markov process, Ann. Probab., 19 (1991), 538-561.
doi: 10.1214/aop/1176990440. |
[12] |
A. D. Ventcel and M. I. Freidlin, On small random perturbations of dynamical systems, Russian Math. Surveys, 25 (1970), 3-55. |
[13] |
A. D. Ventcel, On the asymptotic behavior of the largest eigenvalue of a second-order elliptic differential operator with smaller parameter in the higher derivatives, Theo. Prob. Appl., 20 (1976), 599-602.
doi: 10.1137/1120064. |
[14] |
A. D. Ventcel, Rough limit theorems on large deviations for Markov stochastic processes. I, Theo. Prob. Appl., 21 (1977), 817-821.
doi: 10.1137/1121030. |
show all references
References:
[1] |
J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York, 1984. |
[2] |
G. K. Befekadu, V. Gupta and P. J. Antsaklis, Characterization of feedback Nash equilibria for multi-channel systems via a set of non-fragile stabilizing state-feedback solutions and dissipativity inequalities, J. Math. Contr. Sign. Syst., 25 (2013), 311-326.
doi: 10.1007/s00498-012-0105-z. |
[3] |
M. V. Day, On the exponential exit law in the small parameter exit problem, Stochastics, 8 (1983), 297-323.
doi: 10.1080/17442508308833244. |
[4] |
M. V. Day, Recent progress on the small parameter exit problem, Stochastics, 20 (1987), 121-150.
doi: 10.1080/17442508708833440. |
[5] |
M. V. Day and T. A. Darden, Some regularity results on the Ventcel-Freidlin quasipotential function, Appl. Math. Optim., 13 (1985), 259-282.
doi: 10.1007/BF01442211. |
[6] |
A. Devinatz and A. Friedman, Asymptotic behavior of the principal eigenfunction for a singularly perturbed Dirichlet problem, J. Indiana Univ. Math., 27 (1978), 143-157.
doi: 10.1512/iumj.1978.27.27012. |
[7] |
A. Friedman, Stochastic Differential Equations and Applications, Vol. 2, Academic Press, 1976. |
[8] |
I. L. Glicksberg, A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc., 3 (1952), 170-174. |
[9] |
Y. Kifer, On the principal eigenvalue in a singular perturbation problem with hyperbolic limit points and circles, J. Diff. Equ., 37 (1980), 108-139.
doi: 10.1016/0022-0396(80)90092-3. |
[10] |
Y. Kifer, The inverse problem for small random perturbations of dynamical systems, Israel J. Math., 40 (1981), 165-174.
doi: 10.1007/BF02761907. |
[11] |
S. J. Sheu, Some estimates of the transition density of a non-degenerate diffusion Markov process, Ann. Probab., 19 (1991), 538-561.
doi: 10.1214/aop/1176990440. |
[12] |
A. D. Ventcel and M. I. Freidlin, On small random perturbations of dynamical systems, Russian Math. Surveys, 25 (1970), 3-55. |
[13] |
A. D. Ventcel, On the asymptotic behavior of the largest eigenvalue of a second-order elliptic differential operator with smaller parameter in the higher derivatives, Theo. Prob. Appl., 20 (1976), 599-602.
doi: 10.1137/1120064. |
[14] |
A. D. Ventcel, Rough limit theorems on large deviations for Markov stochastic processes. I, Theo. Prob. Appl., 21 (1977), 817-821.
doi: 10.1137/1121030. |
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