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Le Chen, Yaozhong Hu, Kamran Kalbasi, and David Nualart. Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise. Probab. Theory Related Fields, 171(1-2):431–457, 2018. URL: https://doi.org/10.1007/s00440-017-0783-z, doi:10.1007/s00440-017-0783-z.

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Le Chen, Yaozhong Hu, and David Nualart. Two-point correlation function and Feynman-Kac formula for the stochastic heat equation. Potential Anal., 46(4):779–797, 2017. URL: https://doi.org/10.1007/s11118-016-9601-y, doi:10.1007/s11118-016-9601-y.

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Le Chen, Yaozhong Hu, and David Nualart. Nonlinear stochastic time-fractional slow and fast diffusion equations on $\Bbb R^d$. Stochastic Process. Appl., 129(12):5073–5112, 2019. URL: https://doi.org/10.1016/j.spa.2019.01.003, doi:10.1016/j.spa.2019.01.003.

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Le Chen, Yaozhong Hu, and David Nualart. Regularity and strict positivity of densities for the nonlinear stochastic heat equation. Mem. Amer. Math. Soc., 273(1340):v+102, 2021. URL: https://doi.org/10.1090/memo/1340, doi:10.1090/memo/1340.

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Le Chen and Jingyu Huang. Comparison principle for stochastic heat equation on $\Bbb R^d$. Ann. Probab., 47(2):989–1035, 2019. URL: https://doi.org/10.1214/18-AOP1277, doi:10.1214/18-AOP1277.

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Le Chen and Jingyu Huang. Regularity and strict positivity of densities for the stochastic heat equation on $\mathbb R^d$. Preprint arXiv:1902.02382, February 2019. URL: https://www.arxiv.org/abs/1902.02382.

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Le Chen and Jingyu Huang. Superlinear stochastic heat equation on $\Bbb R^d$. Proc. Amer. Math. Soc., 151(9):4063–4078, 2023. URL: https://doi.org/10.1090/proc/16436, doi:10.1090/proc/16436.

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Le Chen, Jingyu Huang, Davar Khoshnevisan, and Kunwoo Kim. Dense blowup for parabolic SPDEs. Electron. J. Probab., 24:Paper No. 118, 33, 2019. URL: https://doi.org/10.1214/19-ejp372, doi:10.1214/19-ejp372.

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Le Chen, Davar Khoshnevisan, and Kunwoo Kim. Decorrelation of total mass via energy. Potential Anal., 45(1):157–166, 2016. URL: https://doi.org/10.1007/s11118-016-9540-7, doi:10.1007/s11118-016-9540-7.

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Le Chen, Davar Khoshnevisan, and Kunwoo Kim. A boundedness trichotomy for the stochastic heat equation. Ann. Inst. Henri Poincaré Probab. Stat., 53(4):1991–2004, 2017. URL: https://doi.org/10.1214/16-AIHP780, doi:10.1214/16-AIHP780.

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Le Chen, Davar Khoshnevisan, David Nualart, and Fei Pu. A CLT for dependent random variables with an application to an infinite system of interacting diffusion processes. Proc. Amer. Math. Soc., 149(12):5367–5384, 2021. URL: https://doi.org/10.1090/proc/15614, doi:10.1090/proc/15614.

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Le Chen, Davar Khoshnevisan, David Nualart, and Fei Pu. Spatial ergodicity for SPDEs via Poincaré-type inequalities. Electron. J. Probab., 26:Paper No. 140, 37, 2021. URL: https://doi.org/10.1214/21-ejp690, doi:10.1214/21-ejp690.

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Le Chen, Davar Khoshnevisan, David Nualart, and Fei Pu. Central limit theorems for parabolic stochastic partial differential equations. Ann. Inst. Henri Poincaré Probab. Stat., 58(2):1052–1077, 2022. URL: https://doi.org/10.1214/21-aihp1189, doi:10.1214/21-aihp1189.

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Le Chen, Davar Khoshnevisan, David Nualart, and Fei Pu. Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition. J. Funct. Anal., 282(2):Paper No. 109290, 35, 2022. URL: https://doi.org/10.1016/j.jfa.2021.109290, doi:10.1016/j.jfa.2021.109290.

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Le Chen, Davar Khoshnevisan, David Nualart, and Fei Pu. Central limit theorems for spatial averages of the stochastic heat equation via Malliavin-Stein's method. Stoch. Partial Differ. Equ. Anal. Comput., 11(1):122–176, 2023. URL: https://doi.org/10.1007/s40072-021-00224-8, doi:10.1007/s40072-021-00224-8.

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Le Chen and Kunwoo Kim. On comparison principle and strict positivity of solutions to the nonlinear stochastic fractional heat equations. Ann. Inst. Henri Poincaré Probab. Stat., 53(1):358–388, 2017. URL: https://doi.org/10.1214/15-AIHP719, doi:10.1214/15-AIHP719.

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Le Chen and Kunwoo Kim. Nonlinear stochastic heat equation driven by spatially colored noise: moments and intermittency. Acta Math. Sci. Ser. B (Engl. Ed.), 39(3):645–668, 2019. URL: https://doi.org/10.1007/s10473-019-0303-6, doi:10.1007/s10473-019-0303-6.

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Le Chen and Kunwoo Kim. Stochastic comparisons for stochastic heat equation. Electron. J. Probab., 25:Paper No. 140, 38, 2020. URL: https://doi.org/10.1214/20-ejp541, doi:10.1214/20-ejp541.

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Le Chen, Cheng Ouyang, Samy Tindel, and Panqiu Xia. On ergodic properties of stochastic PDEs. Preprint arXiv:2412.03521, December 2024. URL: http://arXiv.org/abs/2412.03521.

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Le Chen, Cheng Ouyang, and William Vickery. Parabolic anderson model with colored noise on torus. Preprint arXiv:2308.10802, to appear in Bernoulli, August 2023. URL: http://arXiv.org/abs/2308.10802.

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Le Chen and Panqiu Xia. Asymptotic properties of stochastic partial differential equations in the sublinear regime. Preprint arXiv:2306.06761, to appear in Annals of Probability, June 2023. URL: http://arXiv.org/abs/2306.06761.

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Xia Chen. Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noise. Ann. Probab., 44(2):1535–1598, 2016. URL: https://doi.org/10.1214/15-AOP1006, doi:10.1214/15-AOP1006.

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Xia Chen. Moment asymptotics for parabolic Anderson equation with fractional time-space noise: in Skorokhod regime. Ann. Inst. Henri Poincaré Probab. Stat., 53(2):819–841, 2017. URL: https://doi.org/10.1214/15-AIHP738, doi:10.1214/15-AIHP738.

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Xia Chen. Parabolic Anderson model with rough or critical Gaussian noise. Ann. Inst. Henri Poincaré Probab. Stat., 55(2):941–976, 2019. URL: https://doi.org/10.1214/18-aihp904, doi:10.1214/18-aihp904.

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Xia Chen, Aurélien Deya, Cheng Ouyang, and Samy Tindel. Moment estimates for some renormalized parabolic Anderson models. Ann. Probab., 49(5):2599–2636, 2021. URL: https://doi.org/10.1214/21-aop1517, doi:10.1214/21-aop1517.

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