-
Previous Article
Attractivity for neutral functional differential equations
- DCDS-B Home
- This Issue
-
Next Article
A Rikitake type system with one control
Derivation of SDES for a macroevolutionary process
1. | Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409-1042, United States, United States |
References:
[1] |
D. J. Aldous, Stochastic models and descriptive statistics for phylogenetic trees from Yule to today, Statistical Science, 16 (2001), 23-34.
doi: 10.1214/ss/998929474. |
[2] |
E. J. Allen, "Modeling with Itô Stochastic Differential Equations," Springer, Dordrecht, 2007. |
[3] |
E. J. Allen, L. J. S. Allen, A. Arciniega and P. E. Greenwood, Construction of equivalent stochastic differential equation models, Stochastic Analysis and Applications, 26 (2008), 274-297.
doi: 10.1080/07362990701857129. |
[4] |
L. J. S. Allen, "An Introduction to Stochastic Processes with Applications to Biology," 2nd edition, CRC Press, Florida, 2011. |
[5] |
T. C. Gard, "Introduction to Stochastic Differential Equations," Marcel Dekker, New York, 1988. |
[6] |
D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, The Journal of Physical Chemistry, 81 (1977), 2340-2361.
doi: 10.1021/j100540a008. |
[7] |
P. E. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations," Springer-Verlag, New York, 1992. |
[8] |
P. E. Kloeden, E. Platen and H. Schurz, "Numerical Solution of SDE Through Computer Experiments," Springer-Verlag, Berlin, 1994.
doi: 10.1007/978-3-642-57913-4. |
[9] |
T. G. Kurtz, Limit theorems for sequences of jump Markov processes approximating ordinary differential equations, The Journal of Applied Probability, 8 (1971), 344-356.
doi: 10.2307/3211904. |
[10] |
P. Langevin, Sur la Théorie du mouvement brownien, Comptes-rendus de l'Académie des Sciences, 146 (1908), 530-533. |
[11] |
C. Semple and M. A. Steel, "Phylogenetics," Oxford University Press, Oxford, 2003. |
[12] |
G. U. Yule, A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, Philosophical Transactions of the Royal Society of London. Series B, 213 (1925), 21-87.
doi: 10.1098/rstb.1925.0002. |
show all references
References:
[1] |
D. J. Aldous, Stochastic models and descriptive statistics for phylogenetic trees from Yule to today, Statistical Science, 16 (2001), 23-34.
doi: 10.1214/ss/998929474. |
[2] |
E. J. Allen, "Modeling with Itô Stochastic Differential Equations," Springer, Dordrecht, 2007. |
[3] |
E. J. Allen, L. J. S. Allen, A. Arciniega and P. E. Greenwood, Construction of equivalent stochastic differential equation models, Stochastic Analysis and Applications, 26 (2008), 274-297.
doi: 10.1080/07362990701857129. |
[4] |
L. J. S. Allen, "An Introduction to Stochastic Processes with Applications to Biology," 2nd edition, CRC Press, Florida, 2011. |
[5] |
T. C. Gard, "Introduction to Stochastic Differential Equations," Marcel Dekker, New York, 1988. |
[6] |
D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, The Journal of Physical Chemistry, 81 (1977), 2340-2361.
doi: 10.1021/j100540a008. |
[7] |
P. E. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations," Springer-Verlag, New York, 1992. |
[8] |
P. E. Kloeden, E. Platen and H. Schurz, "Numerical Solution of SDE Through Computer Experiments," Springer-Verlag, Berlin, 1994.
doi: 10.1007/978-3-642-57913-4. |
[9] |
T. G. Kurtz, Limit theorems for sequences of jump Markov processes approximating ordinary differential equations, The Journal of Applied Probability, 8 (1971), 344-356.
doi: 10.2307/3211904. |
[10] |
P. Langevin, Sur la Théorie du mouvement brownien, Comptes-rendus de l'Académie des Sciences, 146 (1908), 530-533. |
[11] |
C. Semple and M. A. Steel, "Phylogenetics," Oxford University Press, Oxford, 2003. |
[12] |
G. U. Yule, A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, Philosophical Transactions of the Royal Society of London. Series B, 213 (1925), 21-87.
doi: 10.1098/rstb.1925.0002. |
[1] |
Daoyi Xu, Yumei Huang, Zhiguo Yang. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 1005-1023. doi: 10.3934/dcds.2009.24.1005 |
[2] |
Guangjun Shen, Xueying Wu, Xiuwei Yin. Stabilization of stochastic differential equations driven by G-Lévy process with discrete-time feedback control. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 755-774. doi: 10.3934/dcdsb.2020133 |
[3] |
Tomás Caraballo, Carlos Ogouyandjou, Fulbert Kuessi Allognissode, Mamadou Abdoul Diop. Existence and exponential stability for neutral stochastic integro–differential equations with impulses driven by a Rosenblatt process. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : 507-528. doi: 10.3934/dcdsb.2019251 |
[4] |
Shaokuan Chen, Shanjian Tang. Semi-linear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. Mathematical Control and Related Fields, 2015, 5 (3) : 401-434. doi: 10.3934/mcrf.2015.5.401 |
[5] |
Ellina Grigorieva, Evgenii Khailov. A nonlinear controlled system of differential equations describing the process of production and sales of a consumer good. Conference Publications, 2003, 2003 (Special) : 359-364. doi: 10.3934/proc.2003.2003.359 |
[6] |
Ying Hu, Shanjian Tang. Switching game of backward stochastic differential equations and associated system of obliquely reflected backward stochastic differential equations. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5447-5465. doi: 10.3934/dcds.2015.35.5447 |
[7] |
Ludwig Arnold, Igor Chueshov. Cooperative random and stochastic differential equations. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 1-33. doi: 10.3934/dcds.2001.7.1 |
[8] |
Fathalla A. Rihan, Hebatallah J. Alsakaji. Stochastic delay differential equations of three-species prey-predator system with cooperation among prey species. Discrete and Continuous Dynamical Systems - S, 2022, 15 (2) : 245-263. doi: 10.3934/dcdss.2020468 |
[9] |
Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264 |
[10] |
Can Huang, Zhimin Zhang. The spectral collocation method for stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (3) : 667-679. doi: 10.3934/dcdsb.2013.18.667 |
[11] |
Yongqiang Suo, Chenggui Yuan. Large deviations for neutral stochastic functional differential equations. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2369-2384. doi: 10.3934/cpaa.2020103 |
[12] |
Jasmina Djordjević, Svetlana Janković. Reflected backward stochastic differential equations with perturbations. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1833-1848. doi: 10.3934/dcds.2018075 |
[13] |
Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 515-557. doi: 10.3934/dcdsb.2010.14.515 |
[14] |
Jan A. Van Casteren. On backward stochastic differential equations in infinite dimensions. Discrete and Continuous Dynamical Systems - S, 2013, 6 (3) : 803-824. doi: 10.3934/dcdss.2013.6.803 |
[15] |
A. Alamo, J. M. Sanz-Serna. Word combinatorics for stochastic differential equations: Splitting integrators. Communications on Pure and Applied Analysis, 2019, 18 (4) : 2163-2195. doi: 10.3934/cpaa.2019097 |
[16] |
Igor Chueshov, Michael Scheutzow. Invariance and monotonicity for stochastic delay differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1533-1554. doi: 10.3934/dcdsb.2013.18.1533 |
[17] |
Yaozhong Hu, David Nualart, Xiaobin Sun, Yingchao Xie. Smoothness of density for stochastic differential equations with Markovian switching. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3615-3631. doi: 10.3934/dcdsb.2018307 |
[18] |
Pingping Niu, Shuai Lu, Jin Cheng. On periodic parameter identification in stochastic differential equations. Inverse Problems and Imaging, 2019, 13 (3) : 513-543. doi: 10.3934/ipi.2019025 |
[19] |
Joscha Diehl, Jianfeng Zhang. Backward stochastic differential equations with Young drift. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 5-. doi: 10.1186/s41546-017-0016-5 |
[20] |
Xin Chen, Ana Bela Cruzeiro. Stochastic geodesics and forward-backward stochastic differential equations on Lie groups. Conference Publications, 2013, 2013 (special) : 115-121. doi: 10.3934/proc.2013.2013.115 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]