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Interface oscillations in reaction-diffusion systems above the Hopf bifurcation
Optimal harvesting and planting control in stochastic logistic population models
1. | Department of Economics, Matsuyama University, Matsuyama 790-8578, Japan |
References:
[1] |
L. H. R. Alvarez and L. A. Shepp, Optimal harvesting of stochastically fluctuating populations, J. Math. Biol., 37 (1998), 155-177.
doi: 10.1007/s002850050124. |
[2] |
F. H. Clarke, "Optimizationand Nonsmooth Analysis," Canadian Mathematical Society Series of Monographs and Advanced Texts., A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1983. |
[3] |
M. G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27 (1992), 1-67.
doi: 10.1090/S0273-0979-1992-00266-5. |
[4] |
W. H. Fleming and H. M. Soner, "Controlled Markov Processes and Viscosity Solutions," Applications of Mathematics (New York), 25, Springer-Verlag, New York, 1993. |
[5] |
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes," North-Holland Mathematical Library, 24, North-Holland Publishing Co., Amsterdam-New York; Kodansha, Ltd., Tokyo, 1981. |
[6] |
I. Karatzas and S. E. Shreve, "Brownian Motion and Stochastic Calculus," Second edition, Graduate Texts in Mathematics, 113, Springer-Verlag, New York, 1991. |
[7] |
P.-L. Lions and A.-S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 37 (1984), 511-537.
doi: 10.1002/cpa.3160370408. |
[8] |
H. Morimoto, "Stochastic Control and Mathematical Modeling: Applications in Economics," Encyclopedia of Mathematics and its Applications, 131, Cambridge University Press, Cambridge, 2010. |
[9] |
H. Morimoto, A singular control problem with discretionary stopping for geometric Brownian motions, SIAM J. Control Optim., 48 (2010), 3781-3804.
doi: 10.1137/080734856. |
[10] |
S. P. Sethi and M. I. Taksar, Optimal financing of a corporation subject to random returns, Math. Finance, 12 (2002), 155-172.
doi: 10.1111/1467-9965.t01-2-02002. |
[11] |
S. E. Shreve, J. P. Lehoczky and D. P. Gaver, Optimal consumption for general diffusions with absorbing and reflecting barriers, SIAM J. Control Optim., 22 (1984), 55-75.
doi: 10.1137/0322005. |
show all references
References:
[1] |
L. H. R. Alvarez and L. A. Shepp, Optimal harvesting of stochastically fluctuating populations, J. Math. Biol., 37 (1998), 155-177.
doi: 10.1007/s002850050124. |
[2] |
F. H. Clarke, "Optimizationand Nonsmooth Analysis," Canadian Mathematical Society Series of Monographs and Advanced Texts., A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1983. |
[3] |
M. G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27 (1992), 1-67.
doi: 10.1090/S0273-0979-1992-00266-5. |
[4] |
W. H. Fleming and H. M. Soner, "Controlled Markov Processes and Viscosity Solutions," Applications of Mathematics (New York), 25, Springer-Verlag, New York, 1993. |
[5] |
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes," North-Holland Mathematical Library, 24, North-Holland Publishing Co., Amsterdam-New York; Kodansha, Ltd., Tokyo, 1981. |
[6] |
I. Karatzas and S. E. Shreve, "Brownian Motion and Stochastic Calculus," Second edition, Graduate Texts in Mathematics, 113, Springer-Verlag, New York, 1991. |
[7] |
P.-L. Lions and A.-S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 37 (1984), 511-537.
doi: 10.1002/cpa.3160370408. |
[8] |
H. Morimoto, "Stochastic Control and Mathematical Modeling: Applications in Economics," Encyclopedia of Mathematics and its Applications, 131, Cambridge University Press, Cambridge, 2010. |
[9] |
H. Morimoto, A singular control problem with discretionary stopping for geometric Brownian motions, SIAM J. Control Optim., 48 (2010), 3781-3804.
doi: 10.1137/080734856. |
[10] |
S. P. Sethi and M. I. Taksar, Optimal financing of a corporation subject to random returns, Math. Finance, 12 (2002), 155-172.
doi: 10.1111/1467-9965.t01-2-02002. |
[11] |
S. E. Shreve, J. P. Lehoczky and D. P. Gaver, Optimal consumption for general diffusions with absorbing and reflecting barriers, SIAM J. Control Optim., 22 (1984), 55-75.
doi: 10.1137/0322005. |
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