Wang, Jian; Yang, Hao; Zhai, Jianliang; Zhang, Tusheng Large deviation principles for SDEs under locally weak monotonicity conditions. (English) Zbl 07788886 Bernoulli 30, No. 1, 332-345 (2024). Reviewer: Ivan Podvigin (Novosibirsk) MSC: 60F10 60H10 60J25 60K40 92D25 92D30 PDFBibTeX XMLCite \textit{J. Wang} et al., Bernoulli 30, No. 1, 332--345 (2024; Zbl 07788886) Full Text: DOI arXiv
Wu, Weina; Zhai, Jianliang Large deviations for stochastic generalized porous media equations driven by Lévy noise. (English) Zbl 07785711 SIAM J. Math. Anal. 56, No. 1, 1-42 (2024). Reviewer: Oleg K. Zakusilo (Kyïv) MSC: 60F10 60H15 76S05 PDFBibTeX XMLCite \textit{W. Wu} and \textit{J. Zhai}, SIAM J. Math. Anal. 56, No. 1, 1--42 (2024; Zbl 07785711) Full Text: DOI arXiv
Liu, Wei; Song, Yulin; Zhai, Jianliang; Zhang, Tusheng Large and moderate deviation principles for McKean-Vlasov SDEs with jumps. (English) Zbl 1523.60056 Potential Anal. 59, No. 3, 1141-1190 (2023). MSC: 60F10 60H10 60H15 37L55 PDFBibTeX XMLCite \textit{W. Liu} et al., Potential Anal. 59, No. 3, 1141--1190 (2023; Zbl 1523.60056) Full Text: DOI arXiv
Brzeźniak, Zdzisław; Peng, Xuhui; Zhai, Jianliang Well-posedness and large deviations for 2D stochastic Navier-Stokes equations with jumps. (English) Zbl 1519.35220 J. Eur. Math. Soc. (JEMS) 25, No. 8, 3093-3176 (2023). Reviewer: Piotr Biler (Wrocław) MSC: 35Q30 35R60 60F10 60H15 76M35 35B45 35D35 35A01 35A02 35R06 PDFBibTeX XMLCite \textit{Z. Brzeźniak} et al., J. Eur. Math. Soc. (JEMS) 25, No. 8, 3093--3176 (2023; Zbl 1519.35220) Full Text: DOI arXiv
Yang, Juan; Xiang, Ziqiang; Zhai, Jianliang A small time large deviation principle for stochastic differential delay equations. (English) Zbl 1515.60225 Appl. Math. Lett. 143, Article ID 108662, 7 p. (2023). MSC: 60H10 60F10 60J60 34K20 PDFBibTeX XMLCite \textit{J. Yang} et al., Appl. Math. Lett. 143, Article ID 108662, 7 p. (2023; Zbl 1515.60225) Full Text: DOI
Wang, Jian; Zhai, Jianliang; Zhu, Jiahui The stochastic nonlinear Schrödinger equations driven by pure jump noise. (English) Zbl 1518.60061 Stat. Probab. Lett. 197, Article ID 109810, 6 p. (2023). Reviewer: Alain Brillard (Riedisheim) MSC: 60H15 60J76 35B65 35J10 PDFBibTeX XMLCite \textit{J. Wang} et al., Stat. Probab. Lett. 197, Article ID 109810, 6 p. (2023; Zbl 1518.60061) Full Text: DOI arXiv
Wang, Wei; Zhai, Jianliang; Zhang, Tusheng Stochastic two-dimensional Navier-Stokes equations on time-dependent domains. (English) Zbl 1502.35088 J. Theor. Probab. 35, No. 4, 2916-2939 (2022). MSC: 35Q30 76D05 60H15 35D35 35A01 35A02 60J65 35R60 PDFBibTeX XMLCite \textit{W. Wang} et al., J. Theor. Probab. 35, No. 4, 2916--2939 (2022; Zbl 1502.35088) Full Text: DOI
Wang, Wei; Zhai, Jianliang; Zhang, Tusheng Large deviations for stochastic \(2D\) Navier-Stokes equations on time-dependent domains. (English) Zbl 1500.60016 Commun. Pure Appl. Anal. 21, No. 10, 3479-3498 (2022). MSC: 60F10 53C35 35Q30 35R60 60J65 PDFBibTeX XMLCite \textit{W. Wang} et al., Commun. Pure Appl. Anal. 21, No. 10, 3479--3498 (2022; Zbl 1500.60016) Full Text: DOI
Peng, Xuhui; Yang, Juan; Zhai, Jianliang Well-posedness of stochastic 2D hydrodynamics type systems with multiplicative Lévy noises. (English) Zbl 1487.60127 Electron. J. Probab. 27, Paper No. 55, 31 p. (2022). MSC: 60H15 60H07 PDFBibTeX XMLCite \textit{X. Peng} et al., Electron. J. Probab. 27, Paper No. 55, 31 p. (2022; Zbl 1487.60127) Full Text: DOI arXiv
Wang, Ran; Zhai, Jianliang; Zhang, Shiling Large deviation principle for stochastic Burgers type equation with reflection. (English) Zbl 1485.60033 Commun. Pure Appl. Anal. 21, No. 1, 213-238 (2022). Reviewer: Dejun Luo (Beijing) MSC: 60F10 60H15 PDFBibTeX XMLCite \textit{R. Wang} et al., Commun. Pure Appl. Anal. 21, No. 1, 213--238 (2022; Zbl 1485.60033) Full Text: DOI
Wu, Weina; Zhai, Jianliang Stochastic generalized porous media equations driven by Lévy noise with increasing Lipschitz nonlinearities. (English) Zbl 1481.35420 J. Evol. Equ. 21, No. 4, 4845-4871 (2021). MSC: 35R60 35K65 35K90 47D06 PDFBibTeX XMLCite \textit{W. Wu} and \textit{J. Zhai}, J. Evol. Equ. 21, No. 4, 4845--4871 (2021; Zbl 1481.35420) Full Text: DOI arXiv
Zhai, Jianliang; Zhang, Tusheng; Zheng, Wuting Large deviations for stochastic models of two-dimensional second grade fluids driven by Lévy noise. (English) Zbl 1457.60101 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 23, No. 4, Article ID 2050026, 34 p. (2020). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60H15 60F10 35R60 37L55 76M35 PDFBibTeX XMLCite \textit{J. Zhai} et al., Infin. Dimens. Anal. Quantum Probab. Relat. Top. 23, No. 4, Article ID 2050026, 34 p. (2020; Zbl 1457.60101) Full Text: DOI arXiv
Wu, Weina; Zhai, Jianliang Large deviations for stochastic porous media equation on general measure spaces. (English) Zbl 1447.35404 J. Differ. Equations 269, No. 11, 10002-10036 (2020). MSC: 35R60 47D06 PDFBibTeX XMLCite \textit{W. Wu} and \textit{J. Zhai}, J. Differ. Equations 269, No. 11, 10002--10036 (2020; Zbl 1447.35404) Full Text: DOI arXiv
Chen, Lifeng; Dong, Zhao; Jiang, Jifa; Zhai, Jianliang On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity. (English) Zbl 1467.60026 Sci. China, Math. 63, No. 8, 1463-1504 (2020). Reviewer: Ilie Valuşescu (Bucureşti) MSC: 60G10 60H30 60H10 60H15 34K50 37L40 37A25 60G65 60B10 PDFBibTeX XMLCite \textit{L. Chen} et al., Sci. China, Math. 63, No. 8, 1463--1504 (2020; Zbl 1467.60026) Full Text: DOI arXiv
Zhai, Jianliang; Zhang, Tusheng 2D stochastic chemotaxis-Navier-Stokes system. (English. French summary) Zbl 1439.60064 J. Math. Pures Appl. (9) 138, 307-355 (2020). MSC: 60H15 35K55 35K20 92C17 PDFBibTeX XMLCite \textit{J. Zhai} and \textit{T. Zhang}, J. Math. Pures Appl. (9) 138, 307--355 (2020; Zbl 1439.60064) Full Text: DOI arXiv
Sun, Xiaobin; Zhai, Jianliang Averaging principle for stochastic real Ginzburg-Landau equation driven by \(\alpha\)-stable process. (English) Zbl 1431.35259 Commun. Pure Appl. Anal. 19, No. 3, 1291-1319 (2020). MSC: 35R60 60H15 35Q56 PDFBibTeX XMLCite \textit{X. Sun} and \textit{J. Zhai}, Commun. Pure Appl. Anal. 19, No. 3, 1291--1319 (2020; Zbl 1431.35259) Full Text: DOI arXiv
Chen, Lifeng; Dong, Zhao; Jiang, Jifa; Niu, Lei; Zhai, Jianliang Decomposition formula and stationary measures for stochastic Lotka-Volterra system with applications to turbulent convection. (English. French summary) Zbl 1478.60174 J. Math. Pures Appl. (9) 125, 43-93 (2019). MSC: 60H10 60B10 35Q35 37A25 37C29 60G10 PDFBibTeX XMLCite \textit{L. Chen} et al., J. Math. Pures Appl. (9) 125, 43--93 (2019; Zbl 1478.60174) Full Text: DOI arXiv Link
Shang, Shijie; Zhai, Jianliang; Zhang, Tusheng Strong solutions for a stochastic model of two-dimensional second grade fluids driven by Lévy noise. (English) Zbl 1403.60058 J. Math. Anal. Appl. 471, No. 1-2, 126-146 (2019). MSC: 60H15 35R60 35Q30 76A05 PDFBibTeX XMLCite \textit{S. Shang} et al., J. Math. Anal. Appl. 471, No. 1--2, 126--146 (2019; Zbl 1403.60058) Full Text: DOI
Riedle, Markus; Zhai, Jianliang Large deviations for stochastic heat equations with memory driven by Lévy-type noise. (English) Zbl 1431.60064 Discrete Contin. Dyn. Syst. 38, No. 4, 1983-2005 (2018). MSC: 60H15 60F10 37L55 PDFBibTeX XMLCite \textit{M. Riedle} and \textit{J. Zhai}, Discrete Contin. Dyn. Syst. 38, No. 4, 1983--2005 (2018; Zbl 1431.60064) Full Text: DOI arXiv
Zhai, Jianliang; Zhang, Tusheng; Zheng, Wuting Moderate deviations for stochastic models of two-dimensional second grade fluids. (English) Zbl 1396.60075 Stoch. Dyn. 18, No. 3, Article ID 1850026, 46 p. (2018). MSC: 60H15 60F05 60F10 35R60 37L55 PDFBibTeX XMLCite \textit{J. Zhai} et al., Stoch. Dyn. 18, No. 3, Article ID 1850026, 46 p. (2018; Zbl 1396.60075) Full Text: DOI arXiv
Xiong, Jie; Zhai, Jianliang Large deviations for locally monotone stochastic partial differential equations driven by Lévy noise. (English) Zbl 1427.60137 Bernoulli 24, No. 4A, 2842-2874 (2018). MSC: 60H15 35R60 60G51 PDFBibTeX XMLCite \textit{J. Xiong} and \textit{J. Zhai}, Bernoulli 24, No. 4A, 2842--2874 (2018; Zbl 1427.60137) Full Text: DOI arXiv Euclid
Yang, Juan; Zhai, Jianliang Asymptotics of stochastic 2D hydrodynamical type systems in unbounded domains. (English) Zbl 1386.60229 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 20, No. 3, Article ID 1750017, 25 p. (2017). MSC: 60H15 60F05 60F10 PDFBibTeX XMLCite \textit{J. Yang} and \textit{J. Zhai}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 20, No. 3, Article ID 1750017, 25 p. (2017; Zbl 1386.60229) Full Text: DOI arXiv
Zhai, Jianliang; Zhang, Tusheng Large deviations for stochastic models of two-dimensional second grade fluids. (English) Zbl 1370.60049 Appl. Math. Optim. 75, No. 3, 471-498 (2017). MSC: 60F10 60H15 35R60 37L55 76A05 PDFBibTeX XMLCite \textit{J. Zhai} and \textit{T. Zhang}, Appl. Math. Optim. 75, No. 3, 471--498 (2017; Zbl 1370.60049) Full Text: DOI arXiv
Dong, Zhao; Zhai, Jianliang; Zhang, Rangrang Large deviation principles for 3D stochastic primitive equations. (English) Zbl 1370.60103 J. Differ. Equations 263, No. 5, 3110-3146 (2017). Reviewer: Martin Ondreját (Praha) MSC: 60H15 60F10 PDFBibTeX XMLCite \textit{Z. Dong} et al., J. Differ. Equations 263, No. 5, 3110--3146 (2017; Zbl 1370.60103) Full Text: DOI arXiv
Dong, Zhao; Xiong, Jie; Zhai, Jianliang; Zhang, Tusheng A moderate deviation principle for 2-D stochastic Navier-Stokes equations driven by multiplicative Lévy noises. (English) Zbl 1356.60100 J. Funct. Anal. 272, No. 1, 227-254 (2017). Reviewer: Martin Ondreját (Praha) MSC: 60H15 60F10 60G51 60G57 35Q30 PDFBibTeX XMLCite \textit{Z. Dong} et al., J. Funct. Anal. 272, No. 1, 227--254 (2017; Zbl 1356.60100) Full Text: DOI arXiv
Liu, Yong; Zhai, Jianliang Time regularity of generalized Ornstein-Uhlenbeck processes with Lévy noises in Hilbert spaces. (English) Zbl 1390.60244 J. Theor. Probab. 29, No. 3, 843-866 (2016). MSC: 60H15 60J75 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{J. Zhai}, J. Theor. Probab. 29, No. 3, 843--866 (2016; Zbl 1390.60244) Full Text: DOI
Winter, Matthias; Xu, Lihu; Zhai, Jianliang; Zhang, Tusheng The dynamics of the stochastic shadow Gierer-Meinhardt system. (English) Zbl 1337.60139 J. Differ. Equations 260, No. 1, 84-114 (2016). MSC: 60H15 60F10 60J65 60H05 60H30 PDFBibTeX XMLCite \textit{M. Winter} et al., J. Differ. Equations 260, No. 1, 84--114 (2016; Zbl 1337.60139) Full Text: DOI arXiv
Yang, Xue; Zhai, Jianliang; Zhang, Tusheng Large deviations for SPDEs of jump type. (English) Zbl 1327.60074 Stoch. Dyn. 15, No. 4, Article ID 1550026, 30 p. (2015). MSC: 60F10 60H15 60J65 60G57 35R60 37L55 PDFBibTeX XMLCite \textit{X. Yang} et al., Stoch. Dyn. 15, No. 4, Article ID 1550026, 30 p. (2015; Zbl 1327.60074) Full Text: DOI arXiv
Zhai, Jianliang; Zhang, Tusheng Large deviations for 2-D stochastic Navier-Stokes equations driven by multiplicative Lévy noises. (English) Zbl 1344.60030 Bernoulli 21, No. 4, 2351-2392 (2015). Reviewer: Nikolai N. Leonenko (Cardiff) MSC: 60F10 60H15 60G51 60F05 60G55 60G57 60J65 60E07 PDFBibTeX XMLCite \textit{J. Zhai} and \textit{T. Zhang}, Bernoulli 21, No. 4, 2351--2392 (2015; Zbl 1344.60030) Full Text: DOI Euclid
Wang, Ran; Zhai, Jianliang; Zhang, Tusheng A moderate deviation principle for 2-D stochastic Navier-Stokes equations. (English) Zbl 1310.60100 J. Differ. Equations 258, No. 10, 3363-3390 (2015). MSC: 60H15 60F05 60F99 60F10 PDFBibTeX XMLCite \textit{R. Wang} et al., J. Differ. Equations 258, No. 10, 3363--3390 (2015; Zbl 1310.60100) Full Text: DOI
Yang, Juan; Zhai, Jianliang; Zhou, Qing The small time asymptotics of SPDEs with reflection. (English) Zbl 1469.60209 Abstr. Appl. Anal. 2014, Article ID 264263, 13 p. (2014). MSC: 60H15 60F10 PDFBibTeX XMLCite \textit{J. Yang} et al., Abstr. Appl. Anal. 2014, Article ID 264263, 13 p. (2014; Zbl 1469.60209) Full Text: DOI
Liu, Yong; Zhai, Jianliang A note on time regularity of generalized Ornstein-Uhlenbeck processes with cylindrical stable noise. (English. French summary) Zbl 1280.60038 C. R., Math., Acad. Sci. Paris 350, No. 1-2, 97-100 (2012). MSC: 60H15 60J60 PDFBibTeX XMLCite \textit{Y. Liu} and \textit{J. Zhai}, C. R., Math., Acad. Sci. Paris 350, No. 1--2, 97--100 (2012; Zbl 1280.60038) Full Text: DOI
Dong, Zhao; Zhai, Jianliang Martingale solutions and Markov selection of stochastic 3D Navier-Stokes equations with jump. (English) Zbl 1218.60056 J. Differ. Equations 250, No. 6, 2737-2778 (2011). Reviewer: Kai Liu (Liverpool) MSC: 60H15 60J75 60G44 35R60 76D05 60G51 PDFBibTeX XMLCite \textit{Z. Dong} and \textit{J. Zhai}, J. Differ. Equations 250, No. 6, 2737--2778 (2011; Zbl 1218.60056) Full Text: DOI