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

doi:10.1007/s10473-023-0119-2

Abstract

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.

Trendmd

[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^*

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Xiaoxia SUN, Feng GUO. MARTINGALE REPRESENTATION AND LOGARITHMIC-SOBOLEV INEQUALITY FOR THE FRACTIONAL ORNSTEIN-UHLENBECK MEASURE [J]. Acta mathematica scientia,Series B, 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]. Acta mathematica scientia,Series B, 2020, 40(6): 1941-1960.
[3]	Qian YU. A LIMIT LAW FOR FUNCTIONALS OF MULTIPLE INDEPENDENT FRACTIONAL BROWNIAN MOTIONS [J]. Acta mathematica scientia,Series B, 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]. Acta mathematica scientia,Series B, 2019, 39(3): 747-763.
[5]	Yuecai HAN, Yifang SUN. SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS [J]. Acta mathematica scientia,Series B, 2018, 38(2): 681-694.
[6]	Junfeng LIU, Ciprian A. TUDOR. STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE: EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY [J]. Acta mathematica scientia,Series B, 2017, 37(6): 1545-1566.
[7]	Guangjun SHEN, Xiuwei YIN, Litan YAN. ERRATUM TO:LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION [J]. Acta mathematica scientia,Series B, 2017, 37(4): 1173-1176.
[8]	Jing CUI, Litan YAN. CONTROLLABILITY OF NEUTRAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION [J]. Acta mathematica scientia,Series B, 2017, 37(1): 108-118.
[9]	Guangjun SHEN, Xiuwei YIN, Litan YAN. LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION [J]. Acta mathematica scientia,Series B, 2016, 36(2): 394-408.
[10]	SHEN Guang-Jun, YAN Li-Tan, LIU Jun-Feng. POWER VARIATION OF SUBFRACTIONAL BROWNIAN MOTION AND APPLICATION [J]. Acta mathematica scientia,Series B, 2013, 33(4): 901-912.
[11]	WANG Bao-Bin. CONVERGENCE RATE OF MULTIPLE FRACTIONAL STRATONOVICH TYPE INTEGRAL FOR HURST PARAMETER LESS THAN 1/2 [J]. Acta mathematica scientia,Series B, 2011, 31(5): 1694-1708.
[12]	HU Yao-Zhong, Nualart David, XIAO Wei-Lin, ZHANG Wei-Guo. EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION [J]. Acta mathematica scientia,Series B, 2011, 31(5): 1851-1859.
[13]	SHEN Guang-Jun, CHEN Chao, YAN Li-Tan. REMARKS ON SUB-FRACTIONAL BESSEL PROCESSES [J]. Acta mathematica scientia,Series B, 2011, 31(5): 1860-1876.
[14]	HU Yao-Zhong, WANG Bao-Bin. CONVERGENCE RATE OF AN APPROXIMATION TO MULTIPLE INTEGRAL OF FBM [J]. Acta mathematica scientia,Series B, 2010, 30(3): 975-992.
[15]	Lin Zhengyan; Li Degui. STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS [J]. Acta mathematica scientia,Series B, 2008, 28(1): 217-224.