AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE*

doi:10.1007/s10473-023-0119-2

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 349-362.doi: 10.1007/s10473-023-0119-2

AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE^*

Xiuwei YIN

Department of Statistics, Anhui Normal University, Wuhu 241000, China

收稿日期:2021-05-12 修回日期:2022-06-23 发布日期:2023-03-01
基金资助:
*Natural Science Foundation of China (11901005, 12071003) and the Natural Science Foundation of Anhui Province (2008085QA20).

AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE^*

Xiuwei YIN

Department of Statistics, Anhui Normal University, Wuhu 241000, China

Received:2021-05-12 Revised:2022-06-23 Published:2023-03-01
About author:Xiuwei YIN,E-mail: xweiyin@163.com
Supported by:
*Natural Science Foundation of China (11901005, 12071003) and the Natural Science Foundation of Anhui Province (2008085QA20).

摘要/Abstract

摘要： In this paper, we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling. As an application, we also obtain the shift Harnack inequalities.

关键词: integration by parts formula, stochastic heat equations, fractional Brownian motion, shift Harnack inequality, coupling by change of measures

Abstract: In this paper, we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling. As an application, we also obtain the shift Harnack inequalities.

Key words: integration by parts formula, stochastic heat equations, fractional Brownian motion, shift Harnack inequality, coupling by change of measures

Xiuwei YIN. AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE^*[J]. 数学物理学报(英文版), 2023, 43(1): 349-362.

Xiuwei YIN. AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 349-362.

参考文献

[1] Biagini F, Hu Y, Øksendal B, Zhang T.Stochastic Calculus for Fractional Brownian Motions and Applications. Springer, 2008
[2] Boufoussi B, Hajji S.Stochastic delay differential equations in a Hilbert space driven by fractional Brownian motions. Statist Probab Lett, 2017, 129: 222-229
[3] Cui J, Yan L.Controllability of neutral stochastic evolution equation driving by fractional Brownian motions. Acta Math Sci, 2017, 37B(1): 108-118
[4] Decreusefond L, Üstünel A S.Stochastic analysis of the fractional Brownian motions. Potential Anal, 1998, 10: 177-214
[5] Driver B.Integration by parts for heat kernel measures revisited. J Math Pures Appl, 1997, 76: 703-737
[6] Fan X L.Integration by parts formula and applications for SDEs driven by fractional Brownian motions. Stoch Anal Appl, 2015, 33: 199-212
[7] Fan X L.Stochastic Volterra equations driven by fractional Brownian motion. Front Math China, 2015, 10(3): 595-620
[8] Hu Y.Some recent progress on stochastic heat equations. Acta Math Sci, 2019, 39B: 874-914
[9] Hu Y, Nualart D.Stochastic heat equation driven by fractional noise and local time. Prob Theory Related Fields, 2009, 143: 285-328
[10] Huang X, Liu L X, Zhang S Q.Integration by parts formula for SPDEs with multiplicative noise and its applications. Stoch Dyn, 2019, 18(6): 1950024
[11] Mishura Y S.Stochastic calculus for fractional Brownian motions and related processes. Springer, 2008
[12] Nualart D, Ouknine Y.Regularization of quasilinear heat equations by a fractional noise. Stoch Dyn, 2004, 4: 201-221
[13] Wang F Y.Integration by parts formula and shift Harnack inequality for stochastic equations. Ann Probab, 2014, 42: 994-1019
[14] Wang F Y.Integration by parts formula and applications for SPDEs with jumps. Stochastic, 2016, 88: 737-750
[15] Wang F Y.Harnack Inequality for Stochastic Partial Differential Equations. Springer, 2013
[16] Walsh J.An Introduction to SPDEs, École d’été de Probabilités St Flour XIV, Lect Notes in Math, 1180. Springer, 1986
[17] Zhang S Q.Shift Harnack inequality and integration by part formula for semilinear SPDE. Front Math China, 2016, 11: 461-496

AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE^*

AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE^*

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	孙晓霞, 郭峰. MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE[J]. 数学物理学报(英文版), 2021, 41(3): 827-842.
[2]	Soukaina DOUISSI, Khalifa ES-SEBAIY, Soufiane MOUSSATEN. ASYMPTOTICS OF THE CROSS-VARIATION OF YOUNG INTEGRALS WITH RESPECT TO A GENERAL SELF-SIMILAR GAUSSIAN PROCESS[J]. 数学物理学报(英文版), 2020, 40(6): 1941-1960.
[3]	余迁. A LIMIT LAW FOR FUNCTIONALS OF MULTIPLE INDEPENDENT FRACTIONAL BROWNIAN MOTIONS[J]. 数学物理学报(英文版), 2020, 40(3): 734-754.
[4]	Johanna GARZÓN, Samy TINDEL, Soledad TORRES. EULER SCHEME FOR FRACTIONAL DELAY STOCHASTIC DIFFERENTIAL EQUATIONS BY ROUGH PATHS TECHNIQUES[J]. 数学物理学报(英文版), 2019, 39(3): 747-763.
[5]	韩月才, 孙一芳. SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS[J]. 数学物理学报(英文版), 2018, 38(2): 681-694.
[6]	刘俊峰, Ciprian A. TUDOR. STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE: EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY[J]. 数学物理学报(英文版), 2017, 37(6): 1545-1566.
[7]	申广君, 尹修伟, 闫理坦. ERRATUM TO:LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION[J]. 数学物理学报(英文版), 2017, 37(4): 1173-1176.
[8]	崔静, 闫理坦. CONTROLLABILITY OF NEUTRAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION[J]. 数学物理学报(英文版), 2017, 37(1): 108-118.
[9]	申广君, 尹修伟, 闫理坦. LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION[J]. 数学物理学报(英文版), 2016, 36(2): 394-408.
[10]	申广君, 闫理坦, 刘俊峰. POWER VARIATION OF SUBFRACTIONAL BROWNIAN MOTION AND APPLICATION[J]. 数学物理学报(英文版), 2013, 33(4): 901-912.
[11]	汪宝彬. CONVERGENCE RATE OF MULTIPLE FRACTIONAL STRATONOVICH TYPE INTEGRAL FOR HURST PARAMETER LESS THAN 1/2[J]. 数学物理学报(英文版), 2011, 31(5): 1694-1708.
[12]	胡耀忠, Nualart David, 肖炜麟, 张卫国. EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION[J]. 数学物理学报(英文版), 2011, 31(5): 1851-1859.
[13]	申广君, 陈超, 闫理坦. REMARKS ON SUB-FRACTIONAL BESSEL PROCESSES[J]. 数学物理学报(英文版), 2011, 31(5): 1860-1876.
[14]	胡耀忠, 汪宝彬. CONVERGENCE RATE OF AN APPROXIMATION TO MULTIPLE INTEGRAL OF FBM[J]. 数学物理学报(英文版), 2010, 30(3): 975-992.
[15]	林正炎; 李德柜. STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS[J]. 数学物理学报(英文版), 2008, 28(1): 217-224.