Zhang, Bin; Yao, Zhigang; Liu, Junfeng On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise. (English) Zbl 1515.60242 Stat. Probab. Lett. 196, Article ID 109807, 12 p. (2023). MSC: 60H15 60H07 60H30 60G22 PDFBibTeX XMLCite \textit{B. Zhang} et al., Stat. Probab. Lett. 196, Article ID 109807, 12 p. (2023; Zbl 1515.60242) Full Text: DOI
Wang, Wensheng; Chang, Xiaoying; Liao, Wang Asymptotic distributions for power variations of the solution to the spatially colored stochastic heat equation. (English) Zbl 1486.60084 Discrete Dyn. Nat. Soc. 2021, Article ID 8208934, 17 p. (2021). MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{W. Wang} et al., Discrete Dyn. Nat. Soc. 2021, Article ID 8208934, 17 p. (2021; Zbl 1486.60084) Full Text: DOI
Oh, Tadahiro; Okamoto, Mamoru Comparing the stochastic nonlinear wave and heat equations: a case study. (English) Zbl 1469.35270 Electron. J. Probab. 26, Paper No. 9, 44 p. (2021). MSC: 35R60 35K15 35K58 35L15 35L71 60H15 PDFBibTeX XMLCite \textit{T. Oh} and \textit{M. Okamoto}, Electron. J. Probab. 26, Paper No. 9, 44 p. (2021; Zbl 1469.35270) Full Text: DOI arXiv
Assaad, Obayda; Tudor, Ciprian A. Wavelet analysis for the solution to the wave equation with fractional noise in time and white noise in space. (English) Zbl 1478.60120 ESAIM, Probab. Stat. 25, 220-257 (2021). MSC: 60G22 60H07 60H15 62F12 PDFBibTeX XMLCite \textit{O. Assaad} and \textit{C. A. Tudor}, ESAIM, Probab. Stat. 25, 220--257 (2021; Zbl 1478.60120) Full Text: DOI
Mishura, Yuliya; Ralchenko, Kostiantyn; Zili, Mounir; Zougar, Eya Fractional stochastic heat equation with piecewise constant coefficients. (English) Zbl 1476.60076 Stoch. Dyn. 21, No. 1, Article ID 2150002, 39 p. (2021). Reviewer: B. L. S. Prakasa Rao (Hyderabad) MSC: 60G22 60H15 35R60 PDFBibTeX XMLCite \textit{Y. Mishura} et al., Stoch. Dyn. 21, No. 1, Article ID 2150002, 39 p. (2021; Zbl 1476.60076) Full Text: DOI arXiv
Guerngar, Ngartelbaye; Nane, Erkan Moment bounds of a class of stochastic heat equations driven by space-time colored noise in bounded domains. (English) Zbl 1455.60083 Stochastic Processes Appl. 130, No. 10, 6246-6270 (2020). MSC: 60H15 35R11 35R60 60G22 PDFBibTeX XMLCite \textit{N. Guerngar} and \textit{E. Nane}, Stochastic Processes Appl. 130, No. 10, 6246--6270 (2020; Zbl 1455.60083) Full Text: DOI arXiv
Liu, Junfeng Fractional kinetic equation driven by general space-time homogeneous Gaussian noise. (English) Zbl 1422.60059 Bull. Malays. Math. Sci. Soc. (2) 42, No. 6, 3475-3499 (2019). MSC: 60G15 60H15 60H07 PDFBibTeX XMLCite \textit{J. Liu}, Bull. Malays. Math. Sci. Soc. (2) 42, No. 6, 3475--3499 (2019; Zbl 1422.60059) Full Text: DOI
Dozzi, Marco; Touibi, Rim; Vuillermot, Pierre A. Global variational solutions to a class of fractional SPDE’s on unbounded domains. (English) Zbl 1427.60122 Stochastic Anal. Appl. 37, No. 1, 57-73 (2019). MSC: 60H15 60G22 PDFBibTeX XMLCite \textit{M. Dozzi} et al., Stochastic Anal. Appl. 37, No. 1, 57--73 (2019; Zbl 1427.60122) Full Text: DOI arXiv
Lan, Xiaohong; Xiao, Yimin Regularity properties of the solution to a stochastic heat equation driven by a fractional Gaussian noise on \(\mathbb{S}^2\). (English) Zbl 1478.60187 J. Math. Anal. Appl. 476, No. 1, 27-52 (2019). MSC: 60H15 60G22 35B65 35R60 PDFBibTeX XMLCite \textit{X. Lan} and \textit{Y. Xiao}, J. Math. Anal. Appl. 476, No. 1, 27--52 (2019; Zbl 1478.60187) Full Text: DOI arXiv
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
Yan, Litan; Yin, Xiuwei Large deviation principle for a space-time fractional stochastic heat equation with fractional noise. (English) Zbl 1398.60047 Fract. Calc. Appl. Anal. 21, No. 2, 462-485 (2018). MSC: 60F10 60H15 60G22 35R11 PDFBibTeX XMLCite \textit{L. Yan} and \textit{X. Yin}, Fract. Calc. Appl. Anal. 21, No. 2, 462--485 (2018; Zbl 1398.60047) Full Text: DOI
Liu, Junfeng; Tudor, Ciprian A. Generalized Anderson model with time-space multiplicative fractional noise. (English) Zbl 1379.60072 Result. Math. 72, No. 4, 1967-1989 (2017). MSC: 60H15 60H07 60G35 PDFBibTeX XMLCite \textit{J. Liu} and \textit{C. A. Tudor}, Result. Math. 72, No. 4, 1967--1989 (2017; Zbl 1379.60072) Full Text: DOI
Liu, Heng; Chen, Ye; Li, Guanjun; Xiang, Wei; Xu, Guangkui Adaptive fuzzy synchronization of fractional-order chaotic (hyperchaotic) systems with input saturation and unknown parameters. (English) Zbl 1377.93094 Complexity 2017, Article ID 6853826, 16 p. (2017). MSC: 93C42 93C40 34H10 34A08 93D05 PDFBibTeX XMLCite \textit{H. Liu} et al., Complexity 2017, Article ID 6853826, 16 p. (2017; Zbl 1377.93094) Full Text: DOI
Li, Kexue Hölder continuity for stochastic fractional heat equation with colored noise. (English) Zbl 1377.35295 Stat. Probab. Lett. 129, 34-41 (2017). MSC: 35R60 35R11 35K55 35K08 PDFBibTeX XMLCite \textit{K. Li}, Stat. Probab. Lett. 129, 34--41 (2017; Zbl 1377.35295) Full Text: DOI arXiv
Balan, Raluca M.; Jolis, Maria; Quer-Sardanyons, Lluís Intermittency for the hyperbolic Anderson model with rough noise in space. (English) Zbl 1367.60077 Stochastic Processes Appl. 127, No. 7, 2316-2338 (2017). MSC: 60H15 60G15 60G22 60H07 37H15 PDFBibTeX XMLCite \textit{R. M. Balan} et al., Stochastic Processes Appl. 127, No. 7, 2316--2338 (2017; Zbl 1367.60077) Full Text: DOI arXiv
Zhang, Yinghan; Yang, Xiaoyuan Stochastic elastic equation driven by multiplicative multi-parameter fractional noise. (English) Zbl 1360.60128 Stoch. Dyn. 17, No. 2, Article ID 1750012, 22 p. (2017). MSC: 60H15 60G22 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{X. Yang}, Stoch. Dyn. 17, No. 2, Article ID 1750012, 22 p. (2017; Zbl 1360.60128) 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
Bodnarchuk, I. M.; Shevchenko, G. M. Heat equation in a multidimensional domain with a general stochastic measure. (English. Ukrainian original) Zbl 1357.60065 Theory Probab. Math. Stat. 93, 1-17 (2016); translation from Teor. Jmovirn. Mat. Stat. 93, 7-21 (2015). MSC: 60H15 60G17 60G57 PDFBibTeX XMLCite \textit{I. M. Bodnarchuk} and \textit{G. M. Shevchenko}, Theory Probab. Math. Stat. 93, 1--17 (2016; Zbl 1357.60065); translation from Teor. Jmovirn. Mat. Stat. 93, 7--21 (2015) Full Text: DOI
Pryhara, Larysa; Shevchenko, Georgiy Approximations for a solution to stochastic heat equation with stable noise. (English) Zbl 1352.60091 Mod. Stoch., Theory Appl. 3, No. 2, 133-144 (2016). MSC: 60H15 60F15 60G22 60G52 60G57 PDFBibTeX XMLCite \textit{L. Pryhara} and \textit{G. Shevchenko}, Mod. Stoch., Theory Appl. 3, No. 2, 133--144 (2016; Zbl 1352.60091) Full Text: DOI arXiv
Bezdek, Pavel On weak convergence of stochastic heat equation with colored noise. (English) Zbl 1345.60052 Stochastic Processes Appl. 126, No. 9, 2860-2875 (2016). MSC: 60H15 60B10 60F05 PDFBibTeX XMLCite \textit{P. Bezdek}, Stochastic Processes Appl. 126, No. 9, 2860--2875 (2016; Zbl 1345.60052) Full Text: DOI arXiv
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
Liu, Junfeng; Yan, Litan Solving a nonlinear fractional stochastic partial differential equation with fractional noise. (English) Zbl 1335.60114 J. Theor. Probab. 29, No. 1, 307-347 (2016). MSC: 60H15 60G22 60H05 60H07 60G15 PDFBibTeX XMLCite \textit{J. Liu} and \textit{L. Yan}, J. Theor. Probab. 29, No. 1, 307--347 (2016; Zbl 1335.60114) Full Text: DOI
Sun, Xichao; Li, Ming Stochastic fractional heat equations driven by fractional noises. (English) Zbl 1393.60071 Math. Probl. Eng. 2015, Article ID 421705, 16 p. (2015). MSC: 60H15 35R11 35R60 PDFBibTeX XMLCite \textit{X. Sun} and \textit{M. Li}, Math. Probl. Eng. 2015, Article ID 421705, 16 p. (2015; Zbl 1393.60071) Full Text: DOI
Zhang, Yinghan; Yang, Xiaoyuan Fractional stochastic Volterra equation perturbed by fractional Brownian motion. (English) Zbl 1338.45003 Appl. Math. Comput. 256, 20-36 (2015). MSC: 45D05 34A08 45R05 60H20 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{X. Yang}, Appl. Math. Comput. 256, 20--36 (2015; Zbl 1338.45003) Full Text: DOI
Sun, Xichao; Wang, Zhi; Cui, Jing On a fractional SPDE driven by fractional noise and a pure jump Lévy noise in \(\mathbb{R}^d\). (English) Zbl 1474.60166 Abstr. Appl. Anal. 2014, Article ID 758270, 10 p. (2014). MSC: 60H15 35R11 35R60 60J76 PDFBibTeX XMLCite \textit{X. Sun} et al., Abstr. Appl. Anal. 2014, Article ID 758270, 10 p. (2014; Zbl 1474.60166) Full Text: DOI
Hu, Yaozhong; Huang, Jingyu; Nualart, David On Hölder continuity of the solution of stochastic wave equations in dimension three. (English) Zbl 1310.60096 Stoch. Partial Differ. Equ., Anal. Comput. 2, No. 3, 353-407 (2014). MSC: 60H15 60G17 60G22 PDFBibTeX XMLCite \textit{Y. Hu} et al., Stoch. Partial Differ. Equ., Anal. Comput. 2, No. 3, 353--407 (2014; Zbl 1310.60096) 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
Balan, Raluca M. Some linear SPDEs driven by a fractional noise with hurst index greater than 1/2. (English) Zbl 1274.60194 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 15, No. 4, Paper No. 1250023, 27 p. (2012). Reviewer: Martin Ondreját (Praha) MSC: 60H15 60G51 60G22 PDFBibTeX XMLCite \textit{R. M. Balan}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 15, No. 4, Paper No. 1250023, 27 p. (2012; Zbl 1274.60194) Full Text: DOI arXiv
Jorge, León A.; Tindel, Samy Malliavin calculus for fractional delay equations. (English) Zbl 1259.60069 J. Theor. Probab. 25, No. 3, 854-889 (2012). Reviewer: Jacques Franchi (Strasbourg) MSC: 60H20 60H10 60H05 60H07 60G18 60G22 PDFBibTeX XMLCite \textit{L. A. Jorge} and \textit{S. Tindel}, J. Theor. Probab. 25, No. 3, 854--889 (2012; Zbl 1259.60069) Full Text: DOI arXiv
Balan, Raluca M. The stochastic wave equation with multiplicative fractional noise: A Malliavin calculus approach. (English) Zbl 1231.60058 Potential Anal. 36, No. 1, 1-34 (2012). MSC: 60H15 60H07 PDFBibTeX XMLCite \textit{R. M. Balan}, Potential Anal. 36, No. 1, 1--34 (2012; Zbl 1231.60058) Full Text: DOI arXiv
Balan, Raluca M.; Tudor, Ciprian A. The stochastic wave equation with fractional noise: a random field approach. (English) Zbl 1202.60095 Stochastic Processes Appl. 120, No. 12, 2468-2494 (2010). MSC: 60H15 60H05 35R60 PDFBibTeX XMLCite \textit{R. M. Balan} and \textit{C. A. Tudor}, Stochastic Processes Appl. 120, No. 12, 2468--2494 (2010; Zbl 1202.60095) Full Text: DOI arXiv