پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 646 |
| تعداد مقالات | 9,451 |
| تعداد مشاهده مقاله | 68,217,332 |
| تعداد دریافت فایل اصل مقاله | 47,086,619 |
On the pathwise uniqueness for a class of SPDEs driven by Lévy noise in Hilbert spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 15، دوره 15، شماره 1، فروردین 2024، صفحه 179-190 اصل مقاله (412.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.24050.2661 | ||
| نویسندگان | ||
| Majid Zamani؛ S. Mansour Vaezpour* ؛ Erfan Salavati | ||
| Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran | ||
| تاریخ دریافت: 01 مرداد 1400، تاریخ بازنگری: 14 مرداد 1400، تاریخ پذیرش: 10 شهریور 1400 | ||
| چکیده | ||
| This paper seeks to prove the pathwise uniqueness of an abstract stochastic partial differential equation in Hilbert spaces driven by both Poisson random measure and the Wiener process with Hölder continuous drift. The main idea is based on the corresponding infinite-dimensional Kolmogorov equation. In addition, the main result is further supported by the help of an example. | ||
| کلیدواژه‌ها | ||
| Poisson Random Measure؛ Pathwise Uniqueness؛ Infinite Dimensional Kolmogorov Equations؛ Lévy Noise | ||
| مراجع | ||
|
[1] D. Applebaum, Levy processes and stochastic integrals in Banach spaces, Probab. Math. Stat. 27 (2007), 75—88. [2] S. Cerrai, G. Da Prato and F. Flandoli, Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with a Holder drift component, Stoch. Partial Differ. Equ. Anal. Comput. 1 (2013), 507—551. [3] G. Da Prato and F. Flandoli, Pathwise uniqueness for a class of SDE in Hilbert spaces and applications, J. Funct. Anal. 259 (2010), 243-–267. [4] G. Da Prato, F. Flandoli, E. Priola and M. Rockner, Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift, Ann. Probab. 41 (2013), 3306–3344. [5] G. Da Prato, F. Flandoli, E. Priola and M. Rockner, Strong uniqueness for stochastic evolution equations with unbounded measurable drift term, J. Theoret. Probab. 28 (2015), 1571—1600. [6] G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions, Cambridge University Press, UK, 2014. [7] A.M. Davie, Uniqueness of solutions of stochastic differential equations, Int. Math. Res. Not. 2007 (2007), 1—26. [8] E. Fedrizzi and F. Flandoli, Pathwise uniqueness and continuous dependence for SDEs with non-regular drift, Stochastics 83 (2011), 241—257. [9] F. Flandoli, M. Gubinelli and E. Priola, Well-posedness of the transport equation by stochastic perturbation, Invent. Math. 180 (2010), 1–53. [10] I. Gyongy and T. Martınez, On stochastic differential equations with locally unbounded drift, Czechoslovak Math. J. 51 (2001), 763—783. [11] M. Kovacs, F. Lindner and R.L. Schilling, Weak convergence of finite element approximations of linear stochastic evolution equations with additive Levy noise, SIAM/ASA J. Uncertain. Quantif. 3 (2015), 1159—1199. [12] N.V. Krylov and M. Roeckner, Strong solutions of stochastic equations with singular time dependent drift, Probab. Theory Related Fields 131 (2005), 154–196. [13] O. Menoukeu-Pamen, T. Meyer-Brandis, T. Nilssen, F. Proske and T. Zhang, A variational approach to the construction and Malliavin differentiability of strong solutions of SDEs, Math. Ann. 357 (2013), 761–799. [14] S. Peszat and J. Zabczyk, Stochastic Partial Differential Equations with Levy Noise: An Evolution Equation Approach, Cambridge University Press, UK, 2007. [15] E. Priola, Pathwise uniqueness for singular SDEs driven by stable processes, Osaka J. Math. 49 (2012), 421–447. [16] X. Sun, L. Xie and Y. Xie, Pathwise uniqueness for a class of SPDEs driven by cylindrical α-stable processes, Potential Anal. 53 (2020), 659—675. [17] H. Tanaka, M. Tsuchiya and S. Watanabe, Perturbation of drift-type for Levy processes, Kyoto J. Math. 14 (1974), 73–92. [18] A.V. Veretennikov, On the strong solutions of stochastic differential equations, Theory Probab. Appl. 24 (1980), 354–366. [19] D. Yang, Pathwise uniqueness for stochastic evolution equations with Holder drift and stable Levy noise, Nonlinear Differ. Equ. Appl. 25 (2018), 1–7. | ||
|
آمار تعداد مشاهده مقاله: 25,616 تعداد دریافت فایل اصل مقاله: 13,459 |
||