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Zero, one and twoswitch models of gene regulation
1.  Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, Scotland, United Kingdom, United Kingdom 
[1] 
Daoyi Xu, Yumei Huang, Zhiguo Yang. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete & Continuous Dynamical Systems  A, 2009, 24 (3) : 10051023. doi: 10.3934/dcds.2009.24.1005 
[2] 
Kamil Rajdl, Petr Lansky. Fano factor estimation. Mathematical Biosciences & Engineering, 2014, 11 (1) : 105123. doi: 10.3934/mbe.2014.11.105 
[3] 
Qi Wang, Lifang Huang, Kunwen Wen, Jianshe Yu. The mean and noise of stochastic gene transcription with cell division. Mathematical Biosciences & Engineering, 2018, 15 (5) : 12551270. doi: 10.3934/mbe.2018058 
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Yan Wang, Lei Wang, Yanxiang Zhao, Aimin Song, Yanping Ma. A stochastic model for microbial fermentation process under Gaussian white noise environment. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 381392. doi: 10.3934/naco.2015.5.381 
[5] 
Isabelle Kuhwald, Ilya Pavlyukevich. Bistable behaviour of a jumpdiffusion driven by a periodic stablelike additive process. Discrete & Continuous Dynamical Systems  B, 2016, 21 (9) : 31753190. doi: 10.3934/dcdsb.2016092 
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Donny Citra Lesmana, Song Wang. A numerical scheme for pricing American options with transaction costs under a jump diffusion process. Journal of Industrial & Management Optimization, 2017, 13 (4) : 17931813. doi: 10.3934/jimo.2017019 
[7] 
Wuyuan Jiang. The maximum surplus before ruin in a jumpdiffusion insurance risk process with dependence. Discrete & Continuous Dynamical Systems  B, 2019, 24 (7) : 30373050. doi: 10.3934/dcdsb.2018298 
[8] 
Wei Wang, Linyi Qian, Xiaonan Su. Pricing and hedging catastrophe equity put options under a Markovmodulated jump diffusion model. Journal of Industrial & Management Optimization, 2015, 11 (2) : 493514. doi: 10.3934/jimo.2015.11.493 
[9] 
QingQing Yang, WaiKi Ching, Wanhua He, TakKuen Siu. Pricing vulnerable options under a Markovmodulated jumpdiffusion model with fire sales. Journal of Industrial & Management Optimization, 2019, 15 (1) : 293318. doi: 10.3934/jimo.2018044 
[10] 
Ziheng Chen, Siqing Gan, Xiaojie Wang. Meansquare approximations of Lévy noise driven SDEs with superlinearly growing diffusion and jump coefficients. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 45134545. doi: 10.3934/dcdsb.2019154 
[11] 
Kexue Li, Jigen Peng, Junxiong Jia. Explosive solutions of parabolic stochastic partial differential equations with lévy noise. Discrete & Continuous Dynamical Systems  A, 2017, 37 (10) : 51055125. doi: 10.3934/dcds.2017221 
[12] 
David Lipshutz. Exit time asymptotics for small noise stochastic delay differential equations. Discrete & Continuous Dynamical Systems  A, 2018, 38 (6) : 30993138. doi: 10.3934/dcds.2018135 
[13] 
Zhen Li, Jicheng Liu. Synchronization for stochastic differential equations with nonlinear multiplicative noise in the mean square sense. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 128. doi: 10.3934/dcdsb.2019103 
[14] 
Hongjun Gao, Fei Liang. On the stochastic beam equation driven by a NonGaussian Lévy process. Discrete & Continuous Dynamical Systems  B, 2014, 19 (4) : 10271045. doi: 10.3934/dcdsb.2014.19.1027 
[15] 
Lukáš Adam, Jiří Outrata. On optimal control of a sweeping process coupled with an ordinary differential equation. Discrete & Continuous Dynamical Systems  B, 2014, 19 (9) : 27092738. doi: 10.3934/dcdsb.2014.19.2709 
[16] 
Genni Fragnelli, A. Idrissi, L. Maniar. The asymptotic behavior of a population equation with diffusion and delayed birth process. Discrete & Continuous Dynamical Systems  B, 2007, 7 (4) : 735754. doi: 10.3934/dcdsb.2007.7.735 
[17] 
Arnaud Debussche, Sylvain De Moor, Julien Vovelle. Diffusion limit for the radiative transfer equation perturbed by a Wiener process. Kinetic & Related Models, 2015, 8 (3) : 467492. doi: 10.3934/krm.2015.8.467 
[18] 
Xian Chen, ZhiMing Ma. A transformation of Markov jump processes and applications in genetic study. Discrete & Continuous Dynamical Systems  A, 2014, 34 (12) : 50615084. doi: 10.3934/dcds.2014.34.5061 
[19] 
Graeme D. Chalmers, Desmond J. Higham. Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes. Discrete & Continuous Dynamical Systems  B, 2008, 9 (1) : 4764. doi: 10.3934/dcdsb.2008.9.47 
[20] 
Ishak Alia. A nonexponential discounting timeinconsistent stochastic optimal control problem for jumpdiffusion. Mathematical Control & Related Fields, 2019, 9 (3) : 541570. doi: 10.3934/mcrf.2019025 
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