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Stochastic PDE model for spatial population growth in random environments
1. | Department of Mathematics, Wayne State University, Detroit, MI 48202 |
References:
[1] |
P. Chow, Stochastic Partial Differential Equations, $2^{nd}$ edition, Chapman & Hall/CRC, Boca Raton-London-New York, 2015. |
[2] |
P. Chow, Unbounded positive solutions of nonlinear parabolic Itô equations, Comm. Stoch. Analy., 3 (2009), 211-222. |
[3] |
G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
doi: 10.1017/CBO9780511666223. |
[4] |
L. Edelstein-Keshet, Mathematical Models in Biology, Random House, New York, 1988. |
[5] |
I. Gyöngy, N. V. Krylov and B. L. Rozovskii, On stochastic equations with respect to semimartingales II: Itô formula in Banach spacses, Stochastics, 6 (1982), 153-173. |
[6] |
R. Liptser, A strong law of large numbers for local martingales, Stochastics, 3 (1980), 217-228.
doi: 10.1080/17442508008833146. |
[7] |
Y. Lou, T. Nagylaki and W. Ni, An introduction to migration, selection PDE models, Discr. Conti. Dyn. Syst., 33 (2013), 4349-4373.
doi: 10.3934/dcds.2013.33.4349. |
[8] |
X. Mao, S. Sabanis and E. Renshaw, Asymptotic behavier of the sochastic Lotka-Volterra model, J. Math. Analy. Appl., 287 (2003), 141-156.
doi: 10.1016/S0022-247X(03)00539-0. |
[9] |
W. Ni, The Mathematics of Diffusion, CBMS-NSF Regional Conf. Series in Appl. Math., SIAM 82, 2011.
doi: 10.1137/1.9781611971972. |
[10] |
B. Øksendal, Stochastic Differential Equations, Springer, New York, 2003. |
[11] |
E. Pardoux, Stochastic partial differential equations and filtering of diffusion processes, Stochastics, 3 (1979), 127-167.
doi: 10.1080/17442507908833142. |
[12] |
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, Berlin/New York, 1983. |
[13] |
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Walter de Gruyter, Berlin/New York, 1988.
doi: 10.1007/978-1-4684-0313-8. |
[14] |
C. Zhu and G. Yin, On competitive Lotka-Volterra model in random environments, J. Math. Anal. Appl., 357 (2009), 154-170.
doi: 10.1016/j.jmaa.2009.03.066. |
show all references
References:
[1] |
P. Chow, Stochastic Partial Differential Equations, $2^{nd}$ edition, Chapman & Hall/CRC, Boca Raton-London-New York, 2015. |
[2] |
P. Chow, Unbounded positive solutions of nonlinear parabolic Itô equations, Comm. Stoch. Analy., 3 (2009), 211-222. |
[3] |
G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
doi: 10.1017/CBO9780511666223. |
[4] |
L. Edelstein-Keshet, Mathematical Models in Biology, Random House, New York, 1988. |
[5] |
I. Gyöngy, N. V. Krylov and B. L. Rozovskii, On stochastic equations with respect to semimartingales II: Itô formula in Banach spacses, Stochastics, 6 (1982), 153-173. |
[6] |
R. Liptser, A strong law of large numbers for local martingales, Stochastics, 3 (1980), 217-228.
doi: 10.1080/17442508008833146. |
[7] |
Y. Lou, T. Nagylaki and W. Ni, An introduction to migration, selection PDE models, Discr. Conti. Dyn. Syst., 33 (2013), 4349-4373.
doi: 10.3934/dcds.2013.33.4349. |
[8] |
X. Mao, S. Sabanis and E. Renshaw, Asymptotic behavier of the sochastic Lotka-Volterra model, J. Math. Analy. Appl., 287 (2003), 141-156.
doi: 10.1016/S0022-247X(03)00539-0. |
[9] |
W. Ni, The Mathematics of Diffusion, CBMS-NSF Regional Conf. Series in Appl. Math., SIAM 82, 2011.
doi: 10.1137/1.9781611971972. |
[10] |
B. Øksendal, Stochastic Differential Equations, Springer, New York, 2003. |
[11] |
E. Pardoux, Stochastic partial differential equations and filtering of diffusion processes, Stochastics, 3 (1979), 127-167.
doi: 10.1080/17442507908833142. |
[12] |
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, Berlin/New York, 1983. |
[13] |
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Walter de Gruyter, Berlin/New York, 1988.
doi: 10.1007/978-1-4684-0313-8. |
[14] |
C. Zhu and G. Yin, On competitive Lotka-Volterra model in random environments, J. Math. Anal. Appl., 357 (2009), 154-170.
doi: 10.1016/j.jmaa.2009.03.066. |
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