Alfonsi, Aurélien; Kebaier, Ahmed Approximation of stochastic Volterra equations with kernels of completely monotone type. (English) Zbl 07782515 Math. Comput. 93, No. 346, 643-677 (2024). MSC: 60H35 60G22 91G60 45D05 PDFBibTeX XMLCite \textit{A. Alfonsi} and \textit{A. Kebaier}, Math. Comput. 93, No. 346, 643--677 (2024; Zbl 07782515) Full Text: DOI arXiv
Fukasawa, Masaaki; Ugai, Takuto Limit distributions for the discretization error of stochastic Volterra equations with fractional kernel. (English) Zbl 07791530 Ann. Appl. Probab. 33, No. 6B, 5071-5110 (2023). MSC: 60H20 60F17 PDFBibTeX XMLCite \textit{M. Fukasawa} and \textit{T. Ugai}, Ann. Appl. Probab. 33, No. 6B, 5071--5110 (2023; Zbl 07791530) Full Text: DOI arXiv
Fahim, K.; Hausenblas, E.; Kovács, M. Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise. (English) Zbl 07742934 Stoch. Partial Differ. Equ., Anal. Comput. 11, No. 3, 1044-1088 (2023). MSC: 60H20 60G22 65R20 45R05 45D05 45L05 PDFBibTeX XMLCite \textit{K. Fahim} et al., Stoch. Partial Differ. Equ., Anal. Comput. 11, No. 3, 1044--1088 (2023; Zbl 07742934) Full Text: DOI arXiv
Dung, Nguyen Tien; Son, Ta Cong Lipschitz continuity in the Hurst index of the solutions of fractional stochastic Volterra integro-differential equations. (English) Zbl 1515.60243 Stochastic Anal. Appl. 41, No. 4, 693-712 (2023). MSC: 60H20 60G22 60H07 PDFBibTeX XMLCite \textit{N. T. Dung} and \textit{T. C. Son}, Stochastic Anal. Appl. 41, No. 4, 693--712 (2023; Zbl 1515.60243) Full Text: DOI
Bayer, Christian; Breneis, Simon Markovian approximations of stochastic Volterra equations with the fractional kernel. (English) Zbl 1518.91311 Quant. Finance 23, No. 1, 53-70 (2023). MSC: 91G60 65C30 60G22 PDFBibTeX XMLCite \textit{C. Bayer} and \textit{S. Breneis}, Quant. Finance 23, No. 1, 53--70 (2023; Zbl 1518.91311) Full Text: DOI arXiv
Singh, P. K.; Saha Ray, S. Shifted Chebyshev spectral Galerkin method to solve stochastic Itô-Volterra integral equations driven by fractional Brownian motion appearing in mathematical physics. (English) Zbl 07671212 Comput. Appl. Math. 42, No. 3, Paper No. 120, 23 p. (2023). MSC: 65R20 60H30 60H35 45R05 60J65 PDFBibTeX XMLCite \textit{P. K. Singh} and \textit{S. Saha Ray}, Comput. Appl. Math. 42, No. 3, Paper No. 120, 23 p. (2023; Zbl 07671212) Full Text: DOI
Alegría, Francisco; Poblete, Verónica; Pozo, Juan C. Nonlocal in-time telegraph equation and telegraph processes with random time. (English) Zbl 1505.35346 J. Differ. Equations 347, 310-347 (2023). MSC: 35R11 35R60 26A33 45D05 60G22 60H15 60H20 PDFBibTeX XMLCite \textit{F. Alegría} et al., J. Differ. Equations 347, 310--347 (2023; Zbl 1505.35346) Full Text: DOI
Dineshkumar, Chendrayan; Udhayakumar, Ramalingam Results on approximate controllability of fractional stochastic Sobolev-type Volterra-Fredholm integro-differential equation of order \(1 < r < 2\). (English) Zbl 07771059 Math. Methods Appl. Sci. 45, No. 11, 6691-6704 (2022). MSC: 93B05 93E03 26A33 45D05 45J05 PDFBibTeX XMLCite \textit{C. Dineshkumar} and \textit{R. Udhayakumar}, Math. Methods Appl. Sci. 45, No. 11, 6691--6704 (2022; Zbl 07771059) Full Text: DOI
Mahmudov, Nazim I.; Ahmadova, Arzu Some results on backward stochastic differential equations of fractional order. (English) Zbl 1505.34016 Qual. Theory Dyn. Syst. 21, No. 4, Paper No. 129, 23 p. (2022). MSC: 34A08 34F05 47N20 45D05 PDFBibTeX XMLCite \textit{N. I. Mahmudov} and \textit{A. Ahmadova}, Qual. Theory Dyn. Syst. 21, No. 4, Paper No. 129, 23 p. (2022; Zbl 1505.34016) Full Text: DOI arXiv
Wang, Hanxiao; Yong, Jiongmin; Zhang, Jianfeng Path dependent Feynman-Kac formula for forward backward stochastic Volterra integral equations. (English. French summary) Zbl 1494.35071 Ann. Inst. Henri Poincaré, Probab. Stat. 58, No. 2, 603-638 (2022). MSC: 35D40 35K10 35R60 45D05 60G22 60H20 PDFBibTeX XMLCite \textit{H. Wang} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 58, No. 2, 603--638 (2022; Zbl 1494.35071) Full Text: DOI arXiv
Ackermann, Julia; Kruse, Thomas; Overbeck, Ludger Inhomogeneous affine Volterra processes. (English) Zbl 1495.60059 Stochastic Processes Appl. 150, 250-279 (2022). MSC: 60H20 60G22 PDFBibTeX XMLCite \textit{J. Ackermann} et al., Stochastic Processes Appl. 150, 250--279 (2022; Zbl 1495.60059) Full Text: DOI arXiv
Wen, Xiaoxia; Huang, Jin A Haar wavelet method for linear and nonlinear stochastic Itô-Volterra integral equation driven by a fractional Brownian motion. (English) Zbl 1482.60089 Stochastic Anal. Appl. 39, No. 5, 926-943 (2021). MSC: 60H20 60G22 PDFBibTeX XMLCite \textit{X. Wen} and \textit{J. Huang}, Stochastic Anal. Appl. 39, No. 5, 926--943 (2021; Zbl 1482.60089) Full Text: DOI
Prömel, David J.; Trabs, Mathias Paracontrolled distribution approach to stochastic Volterra equations. (English) Zbl 1476.45001 J. Differ. Equations 302, 222-272 (2021). MSC: 45D05 45R05 60H20 60G22 PDFBibTeX XMLCite \textit{D. J. Prömel} and \textit{M. Trabs}, J. Differ. Equations 302, 222--272 (2021; Zbl 1476.45001) Full Text: DOI arXiv
Harang, Fabian A.; Lagunas-Merino, Marc; Ortiz-Latorre, Salvador Self-exciting multifractional processes. (English) Zbl 1464.60035 J. Appl. Probab. 58, No. 1, 22-41 (2021). MSC: 60G22 60H20 60H35 PDFBibTeX XMLCite \textit{F. A. Harang} et al., J. Appl. Probab. 58, No. 1, 22--41 (2021; Zbl 1464.60035) Full Text: DOI arXiv
Knani, Habiba; Dozzi, Marco Linear backward stochastic differential equations with Gaussian Volterra processes. (English) Zbl 1476.35115 Mod. Stoch., Theory Appl. 7, No. 4, 415-433 (2020). MSC: 35K10 60G15 60G22 60H05 60H07 60H10 PDFBibTeX XMLCite \textit{H. Knani} and \textit{M. Dozzi}, Mod. Stoch., Theory Appl. 7, No. 4, 415--433 (2020; Zbl 1476.35115) Full Text: DOI arXiv
Liu, Chan; Wen, Jin; Zhang, Zhidong Reconstruction of the time-dependent source term in a stochastic fractional diffusion equation. (English) Zbl 1464.35399 Inverse Probl. Imaging 14, No. 6, 1001-1024 (2020). MSC: 35R11 35R30 65C30 65M32 PDFBibTeX XMLCite \textit{C. Liu} et al., Inverse Probl. Imaging 14, No. 6, 1001--1024 (2020; Zbl 1464.35399) Full Text: DOI arXiv
Lototsky, S. V.; Rozovsky, B. L. Classical and generalized solutions of fractional stochastic differential equations. (English) Zbl 1461.60049 Stoch. Partial Differ. Equ., Anal. Comput. 8, No. 4, 761-786 (2020). Reviewer: Martin Ondreját (Praha) MSC: 60H15 60H10 60H40 34A08 PDFBibTeX XMLCite \textit{S. V. Lototsky} and \textit{B. L. Rozovsky}, Stoch. Partial Differ. Equ., Anal. Comput. 8, No. 4, 761--786 (2020; Zbl 1461.60049) Full Text: DOI arXiv
Li, Yumeng Central limit theorem for stochastic Volterra equation. (Chinese. English summary) Zbl 1463.60087 Chin. J. Appl. Probab. Stat. 36, No. 2, 173-180 (2020). MSC: 60H20 60F05 PDFBibTeX XMLCite \textit{Y. Li}, Chin. J. Appl. Probab. Stat. 36, No. 2, 173--180 (2020; Zbl 1463.60087) Full Text: DOI
Nane, Erkan; Nwaeze, Eze R.; Omaba, McSylvester Ejighikeme Asymptotic behaviour of solution and non-existence of global solution to a class of conformable time-fractional stochastic equation. (English) Zbl 1448.60146 Stat. Probab. Lett. 163, Article ID 108792, 9 p. (2020). MSC: 60H15 82B44 60G22 PDFBibTeX XMLCite \textit{E. Nane} et al., Stat. Probab. Lett. 163, Article ID 108792, 9 p. (2020; Zbl 1448.60146) Full Text: DOI arXiv
Qi, Ruisheng; Lin, Qiu Time-stepping error bound for a stochastic parabolic Volterra equation disturbed by fractional Brownian motions. (English) Zbl 1449.65256 Numer. Math., Theory Methods Appl. 12, No. 3, 778-796 (2019). MSC: 65M60 65M15 65C30 60G22 33E12 35B65 60H15 35R60 35R11 26A33 45D05 PDFBibTeX XMLCite \textit{R. Qi} and \textit{Q. Lin}, Numer. Math., Theory Methods Appl. 12, No. 3, 778--796 (2019; Zbl 1449.65256) Full Text: DOI
Hausenblas, Erika; Kovács, Mihály Global solutions to stochastic Volterra equations driven by Lévy noise. (English) Zbl 1436.60064 Fract. Calc. Appl. Anal. 21, No. 5, 1170-1202 (2018). MSC: 60H15 60G57 45D05 PDFBibTeX XMLCite \textit{E. Hausenblas} and \textit{M. Kovács}, Fract. Calc. Appl. Anal. 21, No. 5, 1170--1202 (2018; Zbl 1436.60064) Full Text: DOI arXiv
Čoupek, Petr; Maslowski, Bohdan; Šnupárková, Jana SPDEs with Volterra noise. (English) Zbl 1405.60085 Eberle, Andreas (ed.) et al., Stochastic partial differential equations and related fields. In honor of Michael Röckner, SPDERF, Bielefeld, Germany, October 10–14, 2016. Cham: Springer (ISBN 978-3-319-74928-0/hbk; 978-3-319-74929-7/ebook). Springer Proceedings in Mathematics & Statistics 229, 147-158 (2018). MSC: 60H15 60G22 PDFBibTeX XMLCite \textit{P. Čoupek} et al., Springer Proc. Math. Stat. 229, 147--158 (2018; Zbl 1405.60085) Full Text: DOI
Jia, Xiuli; Guan, Lihong Stability in distribution of stochastic Volterra-Levin equations driven by fractional Brownian motion. (Chinese. English summary) Zbl 1399.34171 J. Jilin Univ., Sci. 55, No. 5, 1187-1191 (2017). MSC: 34F05 34D20 60H10 60G22 PDFBibTeX XMLCite \textit{X. Jia} and \textit{L. Guan}, J. Jilin Univ., Sci. 55, No. 5, 1187--1191 (2017; Zbl 1399.34171) Full Text: DOI
Li, Yumeng; Wang, Ran; Yao, Nian; Zhang, Shuguang A moderate deviation principle for stochastic Volterra equation. (English) Zbl 1356.60107 Stat. Probab. Lett. 122, 79-85 (2017). MSC: 60H20 60F10 60F05 60H05 60H10 60G22 PDFBibTeX XMLCite \textit{Y. Li} et al., Stat. Probab. Lett. 122, 79--85 (2017; Zbl 1356.60107) 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
Baeumer, Boris; Geissert, Matthias; Kovács, Mihály Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise. (English) Zbl 1318.60067 J. Differ. Equations 258, No. 2, 535-554 (2015). Reviewer: Ruhollah Jahanipur (Kashan) MSC: 60H15 35R60 35B65 45D05 34A08 PDFBibTeX XMLCite \textit{B. Baeumer} et al., J. Differ. Equations 258, No. 2, 535--554 (2015; Zbl 1318.60067) Full Text: DOI arXiv
Kovács, Mihály; Printems, Jacques Strong order of convergence of a fully discrete approximation of a linear stochastic Volterra type evolution equation. (English) Zbl 1312.60082 Math. Comput. 83, No. 289, 2325-2346 (2014). Reviewer: Jaromir Antoch (Praha) MSC: 60H15 60H35 65C30 65M12 65M60 34A08 45D05 PDFBibTeX XMLCite \textit{M. Kovács} and \textit{J. Printems}, Math. Comput. 83, No. 289, 2325--2346 (2014; Zbl 1312.60082) Full Text: DOI arXiv
Tewfik, Lounis; Said, Bouabdellah Regularisation of the Langevin equation in \(d=1\) by the fractional Brownian motion. (English) Zbl 1260.82066 Adv. Stud. Theor. Phys. 5, No. 9-12, 429-442 (2011). MSC: 82C31 60G22 60J65 60H10 PDFBibTeX XMLCite \textit{L. Tewfik} and \textit{B. Said}, Adv. Stud. Theor. Phys. 5, No. 9--12, 429--442 (2011; Zbl 1260.82066) Full Text: Link
Zhang, Fuqing; Zhang, Qimin The stability of a stochastic Volterra integro-differential equation with fractional Brown motion. (Chinese. English summary) Zbl 1249.60136 J. Cap. Norm. Univ., Nat. Sci. Ed. 32, No. 1, 13-17 (2011). MSC: 60H10 60H20 34D20 60G22 PDFBibTeX XMLCite \textit{F. Zhang} and \textit{Q. Zhang}, J. Cap. Norm. Univ., Nat. Sci. Ed. 32, No. 1, 13--17 (2011; Zbl 1249.60136)
Desch, Wolfgang; Londen, Stig-Olof An \(L_{p }\)-theory for stochastic integral equations. (English) Zbl 1231.60059 J. Evol. Equ. 11, No. 2, 287-317 (2011). MSC: 60H15 60H20 45N05 PDFBibTeX XMLCite \textit{W. Desch} and \textit{S.-O. Londen}, J. Evol. Equ. 11, No. 2, 287--317 (2011; Zbl 1231.60059) Full Text: DOI
Bernyk, Violetta; Dalang, Robert C.; Peskir, Goran Predicting the ultimate supremum of a stable Lévy process with no negative jumps. (English) Zbl 1235.60036 Ann. Probab. 39, No. 6, 2385-2423 (2011). Reviewer: Heinrich Hering (Rockenberg) MSC: 60G40 60J75 45J05 60G25 47G20 26A33 PDFBibTeX XMLCite \textit{V. Bernyk} et al., Ann. Probab. 39, No. 6, 2385--2423 (2011; Zbl 1235.60036) Full Text: DOI arXiv
Bonaccorsi, Stefano Fractional stochastic evolution equations with Lévy noise. (English) Zbl 1240.60193 Differ. Integral Equ. 22, No. 11-12, 1141-1152 (2009). MSC: 60H20 45D05 PDFBibTeX XMLCite \textit{S. Bonaccorsi}, Differ. Integral Equ. 22, No. 11--12, 1141--1152 (2009; Zbl 1240.60193)
Bernyk, Violetta; Dalang, Robert C.; Peskir, Goran The law of the supremum of a stable Lévy process with no negative jumps. (English) Zbl 1185.60051 Ann. Probab. 36, No. 5, 1777-1789 (2008). MSC: 60G52 45D05 60J75 26A33 PDFBibTeX XMLCite \textit{V. Bernyk} et al., Ann. Probab. 36, No. 5, 1777--1789 (2008; Zbl 1185.60051) Full Text: DOI arXiv
Zhang, Xicheng Euler schemes and large deviations for stochastic Volterra equations with singular kernels. (English) Zbl 1139.60329 J. Differ. Equations 244, No. 9, 2226-2250 (2008). MSC: 60H35 60H20 45R05 PDFBibTeX XMLCite \textit{X. Zhang}, J. Differ. Equations 244, No. 9, 2226--2250 (2008; Zbl 1139.60329) Full Text: DOI
Karczewska, Anna; Lizama, Carlos On stochastic fractional Volterra equations in Hilbert space. (English) Zbl 1163.60316 Discrete Contin. Dyn. Syst. 2007, Suppl., 541-550 (2007). MSC: 60H15 60H20 60H05 45D05 PDFBibTeX XMLCite \textit{A. Karczewska} and \textit{C. Lizama}, Discrete Contin. Dyn. Syst. 2007, 541--550 (2007; Zbl 1163.60316) Full Text: arXiv
Buchmann, Boris; Klüppelberg, Claudia Fractional integral equations and state space transforms. (English) Zbl 1114.60048 Bernoulli 12, No. 3, 431-456 (2006). MSC: 60H10 60G10 45D05 PDFBibTeX XMLCite \textit{B. Buchmann} and \textit{C. Klüppelberg}, Bernoulli 12, No. 3, 431--456 (2006; Zbl 1114.60048) Full Text: DOI Euclid
El-Borai, Mahmoud M.; El-Nadi, Khairia El-Said; Mostafa, Osama L.; Ahmed, Hamdy M. Volterra equations with fractional stochastic integrals. (English) Zbl 1081.45007 Math. Probl. Eng. 2004, No. 5, 453-468 (2004). Reviewer: Gong Guanglu (Beijing) MSC: 45R05 60H20 26A33 PDFBibTeX XMLCite \textit{M. M. El-Borai} et al., Math. Probl. Eng. 2004, No. 5, 453--468 (2004; Zbl 1081.45007) Full Text: DOI EuDML
Anh, V. V.; Leonenko, N. N. Harmonic analysis of random fractional diffusion-wave equations. (English) Zbl 1053.60064 Appl. Math. Comput. 141, No. 1, 77-85 (2003). Reviewer: Ismail Taqi Ali (Safat) MSC: 60H15 35C15 26A33 35R10 PDFBibTeX XMLCite \textit{V. V. Anh} and \textit{N. N. Leonenko}, Appl. Math. Comput. 141, No. 1, 77--85 (2003; Zbl 1053.60064) Full Text: DOI
Bonaccorsi, S.; Tubaro, L. Mittag-Leffler’s function and stochastic linear Volterra equations of convolution type. (English) Zbl 1035.60067 Stochastic Anal. Appl. 21, No. 1, 61-78 (2003). Reviewer: Evelyn Buckwar (Berlin) MSC: 60H20 45N05 45R05 45D05 26A33 PDFBibTeX XMLCite \textit{S. Bonaccorsi} and \textit{L. Tubaro}, Stochastic Anal. Appl. 21, No. 1, 61--78 (2003; Zbl 1035.60067) Full Text: DOI
Sinaĭ, Ya. G. Distribution of the maximum of a fractional Brownian motion. (English. Russian original) Zbl 0927.60054 Russ. Math. Surv. 52, No. 2, 359-378 (1997); translation from Usp. Mat. Nauk 52, No. 2, 119-138 (1997). Reviewer: N.M.Zinchenko (Kyïv) MSC: 60G15 60G18 60G17 60J65 PDFBibTeX XMLCite \textit{Ya. G. Sinaĭ}, Russ. Math. Surv. 52, No. 2, 359--378 (1997; Zbl 0927.60054); translation from Usp. Mat. Nauk 52, No. 2, 119--138 (1997) Full Text: DOI