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Preface
Environmental variability and mean-reverting processes
1. | Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409-1042, United States |
References:
[1] |
A. Alfonsi, On the discretization schemes for the CIR (and Bessel squared) processes, Monte Carlo Methods and Applications, 11 (2005), 355-384.
doi: 10.1515/156939605777438569. |
[2] |
A. Alfonsi, Strong convergence of some drift implicit Euler scheme, application to the CIR process, arXiv:1206.3855, (2012). |
[3] |
E. J. Allen, L. J. S. Allen and H. Schurz, A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability, Mathematical Biosciences, 196 (2005), 14-38.
doi: 10.1016/j.mbs.2005.03.010. |
[4] |
E. J. Allen, Modeling With Itô Stochastic Differential Equations, Springer, Dordrecht, The Netherlands, 2007. |
[5] |
L. J. S. Allen and E. J. Allen, A comparison of three different stochastic population models with regard to persistence time, Theoretical Population Biology, 64 (2003), 439-449.
doi: 10.1016/S0040-5809(03)00104-7. |
[6] |
L. J. S. Allen, An Introduction to Stochastic Processes with Applications to Biology, Second edition. CRC Press, Boca Raton, FL, 2011. |
[7] |
F. Black and P. Karasinski, Bond and option pricing when short rates are lognormal, Financial Analysts Journal, 47 (1991), 52-59.
doi: 10.2469/faj.v47.n4.52. |
[8] |
Y. Cai, X. Wang, W. Wang and M. Zhao, Stochastic dynamics of an SIRS epidemic model with ratio-dependent incidence rate, Abstract and Applied Analysis, 2013 (2013), Article ID 172631, 11 pages. |
[9] |
T. C. Gard, Introduction to Stochastic Differential Equations, Marcel Decker, New York, 1988. |
[10] |
A. Gray, D. Greenhalgh, L. Hu, X. Mao and J. Pan, A stochastic differential equation SIS epidemic model, SIAM J. Appl. Math., 71 (2011), 876-902.
doi: 10.1137/10081856X. |
[11] |
P. Hänggi and P. Jung, Colored noise in dynamical systems, Advances in Chemical Physics, 89 (1995), 239-326. |
[12] |
A. S. Hurn, K. A. Lindsay and V. L. Martin, On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential equations, Journal of Time Series Analysis, 24 (2003), 45-63.
doi: 10.1111/1467-9892.00292. |
[13] |
K. Kladívko, Maximum likelihood estimation of the Cox-Ingersoll-Ross process: The MATLAB implementation, Technical Computing Prague, 2007. |
[14] |
P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, New York, 1992.
doi: 10.1007/978-3-662-12616-5. |
[15] |
P. E. Kloeden, E. Platen and H. Schurz, Numerical Solution of SDE Through Computer Experiments, Springer, Berlin, 1994.
doi: 10.1007/978-3-642-57913-4. |
[16] |
C. Kou and S. G. Kou, Modeling growth stocks via birth-death processes, Advances in Applied Probability, 35 (2003), 641-664. |
[17] |
A. G. Ladde and G. S. Ladde, An Introduction to Differential Equations: Stochastic Modeling, Methods and Analysis, Volume 2, World Scientific Publishing Company, Singapore, 2013.
doi: 10.1142/8384. |
[18] |
Y. Lin and D. Jiang, Long-time behavior of a perturbed SIR model by white noise, Discrete and Continuous Dynamical Systems Series B, 18 (2013), 1873-1887.
doi: 10.3934/dcdsb.2013.18.1873. |
[19] |
Q. Lv, M. K. Schneider and J. W. Pitchford, Individualism in plant populations: Using stochastic differential equations to model individual neighbourhood-dependent plant growth, Theoretical Population Biology, 74 (2008), 74-83.
doi: 10.1016/j.tpb.2008.05.003. |
[20] |
X. Mao, C. Yuan and J. Zou, Stochastic differential delay equations of population dynamics, Journal of Mathematical Analysis and Applications, 304 (2005), 296-320.
doi: 10.1016/j.jmaa.2004.09.027. |
[21] |
G. Marion and E Renshaw, Stochastic modelling of environmental variation for biological populations, Theoretical Population Biology, 57 (2000), 197-217.
doi: 10.1006/tpbi.2000.1450. |
[22] |
M. Montero, Predator-Prey Model for Stock Market Fluctuations, arXiv:0810.4844, (2008).
doi: 10.2139/ssrn.1290728. |
[23] |
F. Rao, Dynamical analysis of a stochastic predator-prey model with an alee effect, Abstract and Applied Analysis, 2013 (2013), Article ID 340980, 10 pages. |
[24] |
S. Solomon, Generalized lotka-volterra (GLV) models of stock markets, Advances in Complex Systems, 3 (2000), 301-322.
doi: 10.1142/S0219525900000224. |
[25] |
T. V. Ton and A. Yagi, Dynamics of a stochastic predator-prey model with the Beddington-DeAngelis functional response, Communications on Stochastic Analysis, 5 (2011), 371-386. |
show all references
References:
[1] |
A. Alfonsi, On the discretization schemes for the CIR (and Bessel squared) processes, Monte Carlo Methods and Applications, 11 (2005), 355-384.
doi: 10.1515/156939605777438569. |
[2] |
A. Alfonsi, Strong convergence of some drift implicit Euler scheme, application to the CIR process, arXiv:1206.3855, (2012). |
[3] |
E. J. Allen, L. J. S. Allen and H. Schurz, A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability, Mathematical Biosciences, 196 (2005), 14-38.
doi: 10.1016/j.mbs.2005.03.010. |
[4] |
E. J. Allen, Modeling With Itô Stochastic Differential Equations, Springer, Dordrecht, The Netherlands, 2007. |
[5] |
L. J. S. Allen and E. J. Allen, A comparison of three different stochastic population models with regard to persistence time, Theoretical Population Biology, 64 (2003), 439-449.
doi: 10.1016/S0040-5809(03)00104-7. |
[6] |
L. J. S. Allen, An Introduction to Stochastic Processes with Applications to Biology, Second edition. CRC Press, Boca Raton, FL, 2011. |
[7] |
F. Black and P. Karasinski, Bond and option pricing when short rates are lognormal, Financial Analysts Journal, 47 (1991), 52-59.
doi: 10.2469/faj.v47.n4.52. |
[8] |
Y. Cai, X. Wang, W. Wang and M. Zhao, Stochastic dynamics of an SIRS epidemic model with ratio-dependent incidence rate, Abstract and Applied Analysis, 2013 (2013), Article ID 172631, 11 pages. |
[9] |
T. C. Gard, Introduction to Stochastic Differential Equations, Marcel Decker, New York, 1988. |
[10] |
A. Gray, D. Greenhalgh, L. Hu, X. Mao and J. Pan, A stochastic differential equation SIS epidemic model, SIAM J. Appl. Math., 71 (2011), 876-902.
doi: 10.1137/10081856X. |
[11] |
P. Hänggi and P. Jung, Colored noise in dynamical systems, Advances in Chemical Physics, 89 (1995), 239-326. |
[12] |
A. S. Hurn, K. A. Lindsay and V. L. Martin, On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential equations, Journal of Time Series Analysis, 24 (2003), 45-63.
doi: 10.1111/1467-9892.00292. |
[13] |
K. Kladívko, Maximum likelihood estimation of the Cox-Ingersoll-Ross process: The MATLAB implementation, Technical Computing Prague, 2007. |
[14] |
P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, New York, 1992.
doi: 10.1007/978-3-662-12616-5. |
[15] |
P. E. Kloeden, E. Platen and H. Schurz, Numerical Solution of SDE Through Computer Experiments, Springer, Berlin, 1994.
doi: 10.1007/978-3-642-57913-4. |
[16] |
C. Kou and S. G. Kou, Modeling growth stocks via birth-death processes, Advances in Applied Probability, 35 (2003), 641-664. |
[17] |
A. G. Ladde and G. S. Ladde, An Introduction to Differential Equations: Stochastic Modeling, Methods and Analysis, Volume 2, World Scientific Publishing Company, Singapore, 2013.
doi: 10.1142/8384. |
[18] |
Y. Lin and D. Jiang, Long-time behavior of a perturbed SIR model by white noise, Discrete and Continuous Dynamical Systems Series B, 18 (2013), 1873-1887.
doi: 10.3934/dcdsb.2013.18.1873. |
[19] |
Q. Lv, M. K. Schneider and J. W. Pitchford, Individualism in plant populations: Using stochastic differential equations to model individual neighbourhood-dependent plant growth, Theoretical Population Biology, 74 (2008), 74-83.
doi: 10.1016/j.tpb.2008.05.003. |
[20] |
X. Mao, C. Yuan and J. Zou, Stochastic differential delay equations of population dynamics, Journal of Mathematical Analysis and Applications, 304 (2005), 296-320.
doi: 10.1016/j.jmaa.2004.09.027. |
[21] |
G. Marion and E Renshaw, Stochastic modelling of environmental variation for biological populations, Theoretical Population Biology, 57 (2000), 197-217.
doi: 10.1006/tpbi.2000.1450. |
[22] |
M. Montero, Predator-Prey Model for Stock Market Fluctuations, arXiv:0810.4844, (2008).
doi: 10.2139/ssrn.1290728. |
[23] |
F. Rao, Dynamical analysis of a stochastic predator-prey model with an alee effect, Abstract and Applied Analysis, 2013 (2013), Article ID 340980, 10 pages. |
[24] |
S. Solomon, Generalized lotka-volterra (GLV) models of stock markets, Advances in Complex Systems, 3 (2000), 301-322.
doi: 10.1142/S0219525900000224. |
[25] |
T. V. Ton and A. Yagi, Dynamics of a stochastic predator-prey model with the Beddington-DeAngelis functional response, Communications on Stochastic Analysis, 5 (2011), 371-386. |
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