Egan, Malcolm; Tang, Bao Quoc Macroscopic limit for stochastic chemical reactions involving diffusion and spatial heterogeneity. (English) Zbl 07923199 Stochastic Processes Appl. 176, Article ID 104433, 15 p. (2024). MSC: 60H30 60H15 92E20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Watanabe, Itsuki Continuum limit of nonlocal diffusion on inhomogeneous networks. (English) Zbl 07920479 J. Dyn. Differ. Equations 36, No. 3, 2321-2340 (2024). Reviewer: Ivan Podvigin (Novosibirsk) MSC: 60H30 35K57 60F15 60F05 × Cite Format Result Cite Review PDF Full Text: DOI
Watanabe, Itsuki Markov chain approximation for Hamilton-Jacobi-Bellman equation with absorbing boundary. (English) Zbl 1539.35033 SIAM J. Control Optim. 62, No. 2, 1152-1164 (2024). Reviewer: Rodica Luca (Iaşi) MSC: 35F21 35D40 65N12 60J10 60J76 × Cite Format Result Cite Review PDF Full Text: DOI
Watanabe, Itsuki; Toyoizumi, Hiroshi Comparison between the deterministic and stochastic models of nonlocal diffusion. (English) Zbl 1535.60055 J. Dyn. Differ. Equations 36, No. 1, 231-250 (2024). Reviewer: Weiping Li (Guanghan) MSC: 60F17 60H15 60G15 35K57 × Cite Format Result Cite Review PDF Full Text: DOI
Gao, Hongjun; Liu, Shuaipeng; Xiao, Yeyu The limit behavior of SEIRS model in spatial grid. (English) Zbl 1504.35581 Stoch. Dyn. 22, No. 3, Article ID 2240008, 21 p. (2022). MSC: 35Q92 92D30 35K57 60H10 60H15 60H25 35R60 35A24 × Cite Format Result Cite Review PDF Full Text: DOI
Franco, Tertuliano; Gurgel, Luana; de Lima, Bernardo N. B. Large deviations in the supremum norm for a reaction-diffusion system. (English) Zbl 1490.60270 Braz. J. Probab. Stat. 36, No. 1, 45-80 (2022). MSC: 60K35 60F10 60F17 82C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Debussche, Arnaud; Nguepedja Nankep, Mac Jugal A piecewise deterministic limit for a multiscale stochastic spatial gene network. (English) Zbl 1486.92065 Appl. Math. Optim. 84, Suppl. 2, 1731-1767 (2021). MSC: 92C42 92D10 35Q92 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
N’zi, M.; Pardoux, E.; Yeo, T. A SIR model on a refining spatial grid. I: Law of large numbers. (English) Zbl 1461.92117 Appl. Math. Optim. 83, No. 2, 1153-1189 (2021). MSC: 92D30 35Q92 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lim, Tau Shean; Lu, Yulong; Nolen, James H. Quantitative propagation of chaos in a bimolecular chemical reaction-diffusion model. (English) Zbl 1439.60094 SIAM J. Math. Anal. 52, No. 2, 2098-2133 (2020). MSC: 60K35 35K57 60J60 82C22 90C40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Debussche, Arnaud; Nguepedja Nankep, Mac Jugal A law of large numbers in the supremum norm for a multiscale stochastic spatial gene network. (English) Zbl 07943177 Int. J. Biostat. 15, No. 2, Article ID 20170091, 39 p. (2019). MSC: 62P10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Kaizheng Stochastic representations for the wave equation on graphs and their scaling limits. (English) Zbl 1366.82038 J. Math. Anal. Appl. 449, No. 1, 808-828 (2017). Reviewer: Stylianos Scarlatos (Thessaloniki) MSC: 82C22 60K35 60F17 60J70 60J27 60K40 65C35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Zhen-Qing; Fan, Wai-Tong Louis Fluctuation limit for interacting diffusions with partial annihilations through membranes. (English) Zbl 1350.60101 J. Stat. Phys. 164, No. 4, 890-936 (2016). MSC: 60K35 60J60 60F17 60F05 60H15 60G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Zhen-Qing; Fan, Wai-Tong (Louis) Functional central limit theorem for Brownian particles in domains with Robin boundary condition. (English) Zbl 1342.60044 J. Funct. Anal. 269, No. 12, 3765-3811 (2015). Reviewer: Svetlana Anulova (Moskva) MSC: 60F17 60F05 60H15 60J60 60J65 60J50 60G57 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Riedler, Martin G.; Thieullen, Michèle Spatio-temporal hybrid (PDMP) models: central limit theorem and Langevin approximation for global fluctuations. Application to electrophysiology. (English) Zbl 1327.60063 Bernoulli 21, No. 2, 647-696 (2015). MSC: 60F05 60F17 60F15 60J25 60H15 92C20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Franco, Tertuliano Interacting particle systems: hydrodynamic limit versus high density limit. (English) Zbl 1320.82043 Bernardin, Cedric (ed.) et al., From particle systems to partial differential equations. Proceedings of the conference ‘Particle systems and partial differential equations I’, Braga, Portugal, December 5–7, 2012. Berlin: Springer (ISBN 978-3-642-54270-1/hbk; 978-3-642-54271-8/ebook). Springer Proceedings in Mathematics & Statistics 75, 179-189 (2014). MSC: 82C22 60F05 60F10 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Zhen-Qing; Fan, Wai-Tong Louis Scaling limits of interacting diffusions in domains. (English) Zbl 1308.60108 Front. Math. China 9, No. 4, 717-736 (2014). MSC: 60K35 60J60 60F17 60F05 60H15 60G15 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Franco, Tertuliano; Groisman, Pablo A particle system with explosions: law of large numbers for the density of particles and the blow-up time. (English) Zbl 1260.82040 J. Stat. Phys. 149, No. 4, 629-642 (2012). MSC: 82B41 82B21 35B44 35K58 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Starke, J.; Reichert, C.; Eiswirth, M.; Oelschläger, K. Stochastic modeling and deterministic limit of catalytic surface processes. (English) Zbl 1398.76232 Jäger, Willi (ed.) et al., Reactive flows, diffusion and transport. From experiments via mathematical modeling to numerical simulation and optimization. Final report of SFB (Collaborative Research Center) 359. Berlin: Springer (ISBN 3-540-28379-X/hbk). 341-370 (2007). MSC: 76V05 76M35 80A32 92E20 × Cite Format Result Cite Review PDF Full Text: DOI
Malyshev, V. A. Microscopic models for chemical thermodynamics. (English) Zbl 1079.82009 J. Stat. Phys. 119, No. 5-6, 997-1026 (2005). Reviewer: Chen Mu-Fa (Beijing) MSC: 82C22 60K35 80A30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kouritzin, Michael A.; Long, Hongwei; Sun, Wei Markov chain approximations to filtering equations for reflecting diffusion processes. (English) Zbl 1075.60033 Stochastic Processes Appl. 110, No. 2, 275-294 (2004). Reviewer: Bohdan Maslowski (Praha) MSC: 60G35 60H15 × Cite Format Result Cite Review PDF Full Text: DOI
Gugg, Christoph; Duan, Jinqiao A Markov jump process approximation of the stochastic Burgers equation. (English) Zbl 1095.35082 Stoch. Dyn. 4, No. 2, 245-264 (2004). Reviewer: Nikita E. Ratanov (Bogotá) MSC: 35R60 60H15 82C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kouritzin, Michael A.; Long, Hongwei; Sun, Wei On Markov chain approximations to semilinear partial differential equations driven by Poisson measure noise. (English) Zbl 1079.60062 Stochastic Anal. Appl. 21, No. 2, 419-441 (2003). MSC: 60H15 35K57 35R60 60K37 × Cite Format Result Cite Review PDF Full Text: DOI
Guiaş, Flavius Convergence properties of a stochastic model for coagulation-fragmentation processes with diffusion. (English) Zbl 1015.60094 Stochastic Anal. Appl. 19, No. 2, 245-278 (2001). Reviewer: Martin Janžura (Praha) MSC: 60K35 × Cite Format Result Cite Review PDF Full Text: DOI
Blount, Douglas Diffusion limits for a nonlinear density dependent space-time population model. (English) Zbl 0868.60078 Ann. Probab. 24, No. 2, 639-659 (1996). Reviewer: I.Dôku (Urawa) MSC: 60K35 60H15 60B10 60J60 × Cite Format Result Cite Review PDF Full Text: DOI
Andersson, Håkan; Djehiche, Boualem Limit theorems for multitype epidemics. (English) Zbl 0821.92021 Stochastic Processes Appl. 56, No. 1, 57-75 (1995). Reviewer: A.K.Basu (Calcutta) MSC: 92D30 60B12 60F05 × Cite Format Result Cite Review PDF Full Text: DOI
Penrose, Mathew D. Fluctuations for annihilations of Brownian spheres. (English) Zbl 0806.60064 Stochastic Processes Appl. 51, No. 1, 167-189 (1994). Reviewer: M.Rao (Gainesville) MSC: 60J70 60J65 × Cite Format Result Cite Review PDF Full Text: DOI
Blount, Douglas Limit theorems for a sequence of nonlinear reaction-diffusion systems. (English) Zbl 0773.60052 Stochastic Processes Appl. 45, No. 2, 193-207 (1993). Reviewer: S.Wedrychowicz (Rzeszów) MSC: 60H15 60J80 60J70 60F05 × Cite Format Result Cite Review PDF Full Text: DOI
Fernández, Begoña; Gorostiza, Luis G. Stability of a class of transformations of distribution-valued processes and stochastic evolution equations. (English) Zbl 0762.60053 J. Theor. Probab. 5, No. 4, 661-678 (1992). Reviewer: T.Sasagawa (Tokyo) MSC: 60H15 × Cite Format Result Cite Review PDF Full Text: DOI
Pérez-Abreu, Víctor; Tudor, Constantin Regularity and convergence of stochastic convolutions in duals of nuclear Fréchet spaces. (English) Zbl 0764.60056 J. Multivariate Anal. 43, No. 2, 185-199 (1992). Reviewer: A.F.Gualtierotti (Lausanne) MSC: 60H10 60H20 × Cite Format Result Cite Review PDF Full Text: DOI
Oelschläger, Karl On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes. (English) Zbl 0673.60110 Probab. Theory Relat. Fields 82, No. 4, 565-586 (1989). MSC: 60K35 60J60 × Cite Format Result Cite Review PDF Full Text: DOI
Dittrich, Peter A stochastic particle system: Fluctuations around a nonlinear reaction- diffusion equation. (English) Zbl 0654.60098 Stochastic Processes Appl. 30, No. 1, 149-164 (1988). Reviewer: P.Kotelenez MSC: 60K35 60G57 60F17 60J60 × Cite Format Result Cite Review PDF Full Text: DOI
Kallianpur, G.; Perez-Abreu, V. Stochastic evolution equations driven by nuclear-space-valued martingales. (English) Zbl 0643.60049 Appl. Math. Optimization 17, No. 3, 237-272 (1988). Reviewer: R.Curtain MSC: 60H25 60H10 × Cite Format Result Cite Review PDF Full Text: DOI
Dittrich, P. A stochastic model of a chemical reaction with diffusion. (English) Zbl 0631.60081 Probab. Theory Relat. Fields 79, No. 1, 115-128 (1988). MSC: 60J70 × Cite Format Result Cite Review PDF Full Text: DOI
Kotelenez, Peter High density limit theorems for nonlinear chemical reactions with diffusion. (English) Zbl 0628.60108 Probab. Theory Relat. Fields 78, No. 1, 11-37 (1988). MSC: 60K35 60H15 35K55 60J70 60F17 60F05 60G10 × Cite Format Result Cite Review PDF Full Text: DOI
de Masi, A.; Ferrari, P. A.; Lebowitz, J. L. Reaction-diffusion equations for interacting particle systems. (English) Zbl 0629.60107 J. Stat. Phys. 44, 589-644 (1986). MSC: 60K35 60J70 60J80 82B05 × Cite Format Result Cite Review PDF Full Text: DOI