Han, Yuecai; Wu, Guanyu Feynman-Kac formula for parabolic Anderson model in Gaussian potential and fractional white noise. (English) Zbl 07812219 J. Math. Phys. 65, No. 2, Article ID 021502, 12 p. (2024). MSC: 60H07 60H15 47D08 37L55 PDFBibTeX XMLCite \textit{Y. Han} and \textit{G. Wu}, J. Math. Phys. 65, No. 2, Article ID 021502, 12 p. (2024; Zbl 07812219) Full Text: DOI
Chen, Zhen-Qing; Hu, Yaozhong Solvability of parabolic Anderson equation with fractional Gaussian noise. (English) Zbl 1520.60031 Commun. Math. Stat. 11, No. 3, 563-582 (2023). MSC: 60H15 60G60 60G15 60G22 35R60 PDFBibTeX XMLCite \textit{Z.-Q. Chen} and \textit{Y. Hu}, Commun. Math. Stat. 11, No. 3, 563--582 (2023; Zbl 1520.60031) Full Text: DOI arXiv
Bechtold, Florian Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension. (English) Zbl 1501.35466 Electron. Commun. Probab. 27, Paper No. 47, 13 p. (2022). MSC: 35R60 35K10 60H15 60H50 PDFBibTeX XMLCite \textit{F. Bechtold}, Electron. Commun. Probab. 27, Paper No. 47, 13 p. (2022; Zbl 1501.35466) Full Text: DOI arXiv
Deya, Aurélien; Marty, Renaud A full discretization of the rough fractional linear heat equation. (English) Zbl 07596280 Electron. J. Probab. 27, Paper No. 122, 41 p. (2022). MSC: 65-XX 35K05 35R60 35R11 60H15 60G22 60H35 PDFBibTeX XMLCite \textit{A. Deya} and \textit{R. Marty}, Electron. J. Probab. 27, Paper No. 122, 41 p. (2022; Zbl 07596280) Full Text: DOI arXiv Link
Hong, Jialin; Liu, Zhihui; Sheng, Derui Optimal Hölder continuity and hitting probabilities for SPDEs with rough fractional noises. (English) Zbl 1491.60100 J. Math. Anal. Appl. 512, No. 1, Article ID 126125, 21 p. (2022). MSC: 60H15 60G17 60G22 60H07 PDFBibTeX XMLCite \textit{J. Hong} et al., J. Math. Anal. Appl. 512, No. 1, Article ID 126125, 21 p. (2022; Zbl 1491.60100) Full Text: DOI arXiv
Ma, Nicholas; Nualart, David; Xia, Panqiu Intermittency for the parabolic Anderson model of Skorohod type driven by a rough noise. (English) Zbl 1448.60143 Electron. Commun. Probab. 25, Paper No. 48, 10 p. (2020). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60H15 60G22 60G60 PDFBibTeX XMLCite \textit{N. Ma} et al., Electron. Commun. Probab. 25, Paper No. 48, 10 p. (2020; Zbl 1448.60143) Full Text: DOI arXiv Euclid
Herrell, Randall; Song, Renming; Wu, Dongsheng; Xiao, Yimin Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise. (English) Zbl 1447.60064 Stochastic Anal. Appl. 38, No. 4, 747-768 (2020). MSC: 60G15 60J55 60G18 60F25 PDFBibTeX XMLCite \textit{R. Herrell} et al., Stochastic Anal. Appl. 38, No. 4, 747--768 (2020; Zbl 1447.60064) Full Text: DOI arXiv
Nualart, David; Xia, Panqiu On nonlinear rough paths. (English) Zbl 1443.60083 ALEA, Lat. Am. J. Probab. Math. Stat. 17, No. 1, 545-587 (2020). MSC: 60L20 60H10 60H15 34G20 PDFBibTeX XMLCite \textit{D. Nualart} and \textit{P. Xia}, ALEA, Lat. Am. J. Probab. Math. Stat. 17, No. 1, 545--587 (2020; Zbl 1443.60083) Full Text: arXiv Link
Sun, Xiaobin; Xie, Longjie; Xie, Yingchao Derivative formula for the Feynman-Kac semigroup of SDEs driven by rotationally invariant \(\alpha\)-stable process. (English) Zbl 1439.60057 Stat. Probab. Lett. 158, Article ID 108664, 8 p. (2020). MSC: 60H10 60H20 PDFBibTeX XMLCite \textit{X. Sun} et al., Stat. Probab. Lett. 158, Article ID 108664, 8 p. (2020; Zbl 1439.60057) Full Text: DOI
Hu, Yaozhong Some recent progress on stochastic heat equations. (English) Zbl 1499.60220 Acta Math. Sci., Ser. B, Engl. Ed. 39, No. 3, 874-914 (2019). MSC: 60H15 35K15 35R60 PDFBibTeX XMLCite \textit{Y. Hu}, Acta Math. Sci., Ser. B, Engl. Ed. 39, No. 3, 874--914 (2019; Zbl 1499.60220) Full Text: DOI
Hu, Yaozhong; Liu, Yanghui; Tindel, Samy On the necessary and sufficient conditions to solve a heat equation with general additive Gaussian noise. (English) Zbl 1499.60222 Acta Math. Sci., Ser. B, Engl. Ed. 39, No. 3, 669-690 (2019). MSC: 60H15 60G15 60H07 PDFBibTeX XMLCite \textit{Y. Hu} et al., Acta Math. Sci., Ser. B, Engl. Ed. 39, No. 3, 669--690 (2019; Zbl 1499.60222) Full Text: DOI arXiv
Li, Heyu; Chen, Xia Precise moment asymptotics for the stochastic heat equation of a time-derivative Gaussian noise. (English) Zbl 1499.60226 Acta Math. Sci., Ser. B, Engl. Ed. 39, No. 3, 629-644 (2019). MSC: 60H15 60F10 35R60 35K15 PDFBibTeX XMLCite \textit{H. Li} and \textit{X. Chen}, Acta Math. Sci., Ser. B, Engl. Ed. 39, No. 3, 629--644 (2019; Zbl 1499.60226) Full Text: DOI
Saravanakumar, S.; Balasubramaniam, P. On impulsive Hilfer fractional stochastic differential system driven by Rosenblatt process. (English) Zbl 1428.34022 Stochastic Anal. Appl. 37, No. 6, 955-976 (2019). MSC: 34A08 60H10 34G20 34F05 47N20 34A37 PDFBibTeX XMLCite \textit{S. Saravanakumar} and \textit{P. Balasubramaniam}, Stochastic Anal. Appl. 37, No. 6, 955--976 (2019; Zbl 1428.34022) Full Text: DOI
Deya, Aurélien A nonlinear wave equation with fractional perturbation. (English) Zbl 1427.60121 Ann. Probab. 47, No. 3, 1775-1810 (2019). MSC: 60H15 60G22 35L71 PDFBibTeX XMLCite \textit{A. Deya}, Ann. Probab. 47, No. 3, 1775--1810 (2019; Zbl 1427.60121) Full Text: DOI arXiv Euclid
Xia, Dengfeng; Yan, Litan; Yin, Xiuwei On a semilinear double fractional heat equation driven by fractional Brownian sheet. (English) Zbl 1456.60163 J. Appl. Anal. Comput. 8, No. 1, 202-228 (2018). MSC: 60H15 60F10 60G22 PDFBibTeX XMLCite \textit{D. Xia} et al., J. Appl. Anal. Comput. 8, No. 1, 202--228 (2018; Zbl 1456.60163) Full Text: DOI
Chen, Le; Hu, Yaozhong; Kalbasi, Kamran; Nualart, David Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise. (English) Zbl 1391.60153 Probab. Theory Relat. Fields 171, No. 1-2, 431-457 (2018). MSC: 60H15 60G60 35R60 PDFBibTeX XMLCite \textit{L. Chen} et al., Probab. Theory Relat. Fields 171, No. 1--2, 431--457 (2018; Zbl 1391.60153) Full Text: DOI arXiv
Tamilalagan, P.; Balasubramaniam, P. Moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional Brownian motion. (English) Zbl 1411.60089 Appl. Math. Comput. 305, 299-307 (2017). MSC: 60H10 34F05 34A08 34G25 34K09 34K50 47H10 60G22 PDFBibTeX XMLCite \textit{P. Tamilalagan} and \textit{P. Balasubramaniam}, Appl. Math. Comput. 305, 299--307 (2017; Zbl 1411.60089) Full Text: DOI
Xia, Dengfeng; Yan, Litan Some properties of the solution to fractional heat equation with a fractional Brownian noise. (English) Zbl 1422.35180 Adv. Difference Equ. 2017, Paper No. 107, 16 p. (2017). MSC: 35R11 60H15 60H07 26A33 PDFBibTeX XMLCite \textit{D. Xia} and \textit{L. Yan}, Adv. Difference Equ. 2017, Paper No. 107, 16 p. (2017; Zbl 1422.35180) Full Text: DOI
Xia, Dengfeng; Yan, Litan On a semilinear mixed fractional heat equation driven by fractional Brownian sheet. (English) Zbl 1355.60087 Bound. Value Probl. 2017, Paper No. 7, 24 p. (2017). MSC: 60H15 60G22 60H07 PDFBibTeX XMLCite \textit{D. Xia} and \textit{L. Yan}, Bound. Value Probl. 2017, Paper No. 7, 24 p. (2017; Zbl 1355.60087) Full Text: DOI
Hu, Yaozhong; Lê, Khoa Nonlinear Young integrals and differential systems in Hölder media. (English) Zbl 1356.60086 Trans. Am. Math. Soc. 369, No. 3, 1935-2002 (2017). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60H05 60H15 60H10 60H30 60H07 60G60 60G15 60G17 60J60 PDFBibTeX XMLCite \textit{Y. Hu} and \textit{K. Lê}, Trans. Am. Math. Soc. 369, No. 3, 1935--2002 (2017; Zbl 1356.60086) Full Text: DOI arXiv
Cui, Jing; Wang, Zhi Nonlocal stochastic integro-differential equations driven by fractional Brownian motion. (English) Zbl 1419.60050 Adv. Difference Equ. 2016, Paper No. 115, 14 p. (2016). MSC: 60H15 60H20 34K37 PDFBibTeX XMLCite \textit{J. Cui} and \textit{Z. Wang}, Adv. Difference Equ. 2016, Paper No. 115, 14 p. (2016; Zbl 1419.60050) Full Text: DOI
Balan, Raluca M.; Conus, Daniel Intermittency for the wave and heat equations with fractional noise in time. (English) Zbl 1343.60081 Ann. Probab. 44, No. 2, 1488-1534 (2016). Reviewer: Martin Ondreját (Praha) MSC: 60H15 60H07 60G22 PDFBibTeX XMLCite \textit{R. M. Balan} and \textit{D. Conus}, Ann. Probab. 44, No. 2, 1488--1534 (2016; Zbl 1343.60081) Full Text: DOI arXiv Euclid
Yu, Xianye; Sun, Xichao; Yan, Litan Solving a stochastic heat equation driven by a bi-fractional noise. (English) Zbl 1338.60109 Bound. Value Probl. 2016, Paper No. 66, 22 p. (2016). MSC: 60G15 60H05 60G17 PDFBibTeX XMLCite \textit{X. Yu} et al., Bound. Value Probl. 2016, Paper No. 66, 22 p. (2016; Zbl 1338.60109) Full Text: DOI
Kalbasi, Kamran; Mountford, Thomas S. Feynman-Kac representation for the parabolic Anderson model driven by fractional noise. (English) Zbl 1322.60115 J. Funct. Anal. 269, No. 5, 1234-1263 (2015). MSC: 60H15 60G22 60G50 PDFBibTeX XMLCite \textit{K. Kalbasi} and \textit{T. S. Mountford}, J. Funct. Anal. 269, No. 5, 1234--1263 (2015; Zbl 1322.60115) Full Text: DOI arXiv
Balan, Raluca M.; Conus, Daniel A note on intermittency for the fractional heat equation. (English) Zbl 1300.60077 Stat. Probab. Lett. 95, 6-14 (2014). MSC: 60H15 35R11 37H15 60H07 PDFBibTeX XMLCite \textit{R. M. Balan} and \textit{D. Conus}, Stat. Probab. Lett. 95, 6--14 (2014; Zbl 1300.60077) Full Text: DOI arXiv
Zhang, Hong; Li, Guo-Hua; Luo, Mao-Kang Fractional Feynman-Kac equation with space-dependent anomalous exponent. (English) Zbl 1277.82043 J. Stat. Phys. 152, No. 6, 1194-1206 (2013). MSC: 82C31 35R11 35Q84 82C41 60J75 60J60 PDFBibTeX XMLCite \textit{H. Zhang} et al., J. Stat. Phys. 152, No. 6, 1194--1206 (2013; Zbl 1277.82043) Full Text: DOI
Hu, Yaozhong; Nualart, David; Song, Jian Feynman-Kac formula for heat equation driven by fractional white noise. (English) Zbl 1210.60056 Ann. Probab. 39, No. 1, 291-326 (2011). Reviewer: Carles Rovira (Barcelona) MSC: 60H07 60H15 60G17 60G22 60G30 35K20 35R60 PDFBibTeX XMLCite \textit{Y. Hu} et al., Ann. Probab. 39, No. 1, 291--326 (2011; Zbl 1210.60056) Full Text: DOI arXiv