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Volumn 9, Issue 2, 2009, Pages 235-265

Mild solutions for a class of fractional SPDEs and their sample paths

Author keywords

Fractional Brownian motion; Green's function; Sample path regularity; Stochastic partialdifferential equation

Indexed keywords


EID: 67349259392     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-009-0014-x     Document Type: Article
Times cited : (20)

References (38)
  • 2
    • 0035537291 scopus 로고    scopus 로고
    • Stochastic Calculus with respect to Gaussian Processes
    • E. Alòs O. Mazet D. Nualart 2001 Stochastic Calculus with respect to Gaussian Processes The Annals of Probability 29 766 801
    • (2001) The Annals of Probability , vol.29 , pp. 766-801
    • Alòs, E.1    Mazet, O.2    Nualart, D.3
  • 3
    • 34547179020 scopus 로고    scopus 로고
    • A Version of Hörmander's Theorem for the Fractional Brownian Motion Probab
    • F. Baudoin M. Hairer 2007 A Version of Hörmander's Theorem for the Fractional Brownian Motion Probab Theory and Related Fields 139 373 395
    • (2007) Theory and Related Fields , vol.139 , pp. 373-395
    • Baudoin, F.1    Hairer, M.2
  • 4
    • 33644937071 scopus 로고    scopus 로고
    • Notes on the Two-Dimensional Fractional Brownian Motion
    • F. Baudoin D. Nualart 2006 Notes on the Two-Dimensional Fractional Brownian Motion The Annals of Probability 34 159 180
    • (2006) The Annals of Probability , vol.34 , pp. 159-180
    • Baudoin, F.1    Nualart, D.2
  • 6
    • 0001241006 scopus 로고
    • Regularity of Solutions of Linear Stochastic Equations in Hilbert Spaces
    • G. Da Prato S. Kwapien J. Zabczyk 1987 Regularity of Solutions of Linear Stochastic Equations in Hilbert Spaces Stochastics 23 1 23
    • (1987) Stochastics , vol.23 , pp. 1-23
    • Da Prato, G.1    Kwapien, S.2    Zabczyk, J.3
  • 7
    • 0036100640 scopus 로고    scopus 로고
    • Regularity properties of some stochastic Volterra integrals with singular kernel
    • DOI 10.1023/A:1012628013041
    • L. Decreusefond 2002 Regularity Properties of Some Stochastic Volterra Integrals with Singular Kernel Potential Analysis 16 139 149 (Pubitemid 37132682)
    • (2002) Potential Analysis , vol.16 , Issue.2 , pp. 139-149
    • Decreusefond, L.1
  • 8
    • 0042637937 scopus 로고    scopus 로고
    • Stochastic Analysis of the Fractional Brownian Motion
    • L. Decreusefond A.S. Üstünel 1999 Stochastic Analysis of the Fractional Brownian Motion Potential Analysis 10 177 214
    • (1999) Potential Analysis , vol.10 , pp. 177-214
    • Decreusefond, L.1    Üstünel, A.S.2
  • 9
    • 8744274079 scopus 로고    scopus 로고
    • A general analytical result for non-linear SPDE's and applications
    • L. Denis L. Stoica 2004 A General Analytical Result for Non-Linear SPDE's and Applications Electronic J. of Probability 9 674 709 (Pubitemid 39520692)
    • (2004) Electronic Journal of Probability , vol.9 , pp. 674-709
    • Denis, L.1    Stoica, L.2
  • 10
    • 34547972571 scopus 로고    scopus 로고
    • Transient Noise Simulation: Modeling and Simulation of 1/f Noise
    • Modeling, Simulation and Optimization of Integrated Circuits Birkhäuser, Basel
    • G. Denk, D. Meintrup, S. Schäffler, Transient Noise Simulation: Modeling and Simulation of 1/f -Noise,in: Modeling, Simulation and Optimization of Integrated Circuits, Internat. Ser. Numer. Math., Vol. 146 (2003) 251-267, Birkhäuser, Basel.
    • (2003) Internat. Ser. Numer. Math. , vol.146 , pp. 251-267
    • Denk, G.1
  • 12
    • 19344371593 scopus 로고    scopus 로고
    • Approximations of the Brownian rough path with applications to stochastic analysis
    • DOI 10.1016/j.anihpb.2004.05.003, PII S0246020304000603
    • P. Friz N. Victoir 2005 Approximations of the Brownian Rough Path with Applications to Stochastic Analysis Ann. I. H. Poincaré-PR 41 703 724 (Pubitemid 40721625)
    • (2005) Annales de l'institut Henri Poincare (B) Probability and Statistics , vol.41 , Issue.4 , pp. 703-724
    • Friz, P.1    Victoir, N.2
  • 16
    • 1642380843 scopus 로고    scopus 로고
    • General Fractional Multiparameter White Noise Theory and Stochastic Partial Differential Equations
    • Y. Hu B. Oksendal T. Zhang 2004 General Fractional Multiparameter White Noise Theory and Stochastic Partial Differential Equations Comm. Partial Differential Equations 29 1 23 (Pubitemid 38389558)
    • (2004) Communications in Partial Differential Equations , vol.29 , Issue.1-2 , pp. 1-23
    • Hu, Y.1    Oksendal, B.2    Zhang, T.3
  • 17
    • 22644449415 scopus 로고    scopus 로고
    • Ordinary Differential Equations with Fractal Noise
    • F. Klingenhöfer M. Zähle 1999 Ordinary Differential Equations with Fractal Noise Proc. Amer. Math. Soc. 127 1021 1028
    • (1999) Proc. Amer. Math. Soc. , vol.127 , pp. 1021-1028
    • Klingenhöfer, F.1    Zähle, M.2
  • 18
    • 0001187166 scopus 로고
    • Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum
    • A.N. Kolmogorov 1940 Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum C. R. Acad. URSS 26 115 118
    • (1940) C. R. Acad. URSS , vol.26 , pp. 115-118
    • Kolmogorov, A.N.1
  • 20
    • 0003223550 scopus 로고
    • Linear and Quasilinear Equations of Parabolic Type
    • American Mathematical Society, Providence, RI
    • O. Ladyzenskaya, N. Uraltceva, V.A. Solonnikov, Linear and Quasilinear Equations of Parabolic Type in: AMS-Transl. of Math. Monographs, Vol. 23 (1968) American Mathematical Society, Providence, RI.
    • (1968) AMS-Transl. of Math. Monographs , vol.23
    • Ladyzenskaya, O.1    Uraltceva, N.2    Solonnikov, V.A.3
  • 23
    • 0000501589 scopus 로고
    • Fractional Brownian Motions, Fractional Noises and Applications
    • B.B. Mandelbrot J.W. Van Ness 1968 Fractional Brownian Motions, Fractional Noises and Applications SIAM Rev. 10 422 437
    • (1968) SIAM Rev. , vol.10 , pp. 422-437
    • Mandelbrot, B.B.1    Van Ness, J.W.2
  • 24
    • 0042229456 scopus 로고    scopus 로고
    • Evolution equations driven by a fractional Brownian motion
    • DOI 10.1016/S0022-1236(02)00065-4, PII S0022123602000654
    • B. Maslowski D. Nualart 2003 Evolution Equations driven by a Fractional Brownian Motion Journal of Functional Analysis 202 277 305 (Pubitemid 36989400)
    • (2003) Journal of Functional Analysis , vol.202 , Issue.1 , pp. 277-305
    • Maslowski, B.1    Nualart, D.2
  • 26
    • 58149204320 scopus 로고    scopus 로고
    • The Malliavin Calculus and Related Topics
    • Springer, New York
    • D. Nualart, The Malliavin Calculus and Related Topics,in: Probability and its Applications (2006) Springer, New York.
    • (2006) Probability and Its Applications
    • Nualart, D.1
  • 27
    • 14944377936 scopus 로고    scopus 로고
    • Central limit theorems for sequences of multiple stochastic integrals
    • DOI 10.1214/009117904000000621
    • D. Nualart G. Peccati 2005 Central Limit Theorems for Sequences of Multiple Stochastic Integrals The Annals of Probability 33 177 193 (Pubitemid 40367061)
    • (2005) Annals of Probability , vol.33 , Issue.1 , pp. 177-193
    • Nualart, D.1    Peccati, G.2
  • 28
    • 0038771348 scopus 로고    scopus 로고
    • Differential Equations driven by Fractional Brownian Motion
    • D. Nualart A. Rǎşcanu 2002 Differential Equations driven by Fractional Brownian Motion Collect. Math. 53 55 81
    • (2002) Collect. Math. , vol.53 , pp. 55-81
    • Nualart, D.1    Rǎşcanu, A.2
  • 29
    • 31744433902 scopus 로고    scopus 로고
    • Variational solutions for partial differential equations driven by a fractional noise
    • DOI 10.1016/j.jfa.2005.06.015, PII S0022123605002594
    • D. Nualart P.-A. Vuillermot 2006 Variational Solutions for Partial Differential Equations driven by a Fractional Noise Journal of Functional Analysis 232 390 454 (Pubitemid 43174886)
    • (2006) Journal of Functional Analysis , vol.232 , Issue.2 , pp. 390-454
    • Nualart, D.1    Vuillermot, P.-A.2
  • 31
    • 0034562433 scopus 로고    scopus 로고
    • Integration questions related to fractional Brownian motion
    • DOI 10.1007/s440-000-8016-7
    • V. Pipiras M.S. Taqqu 2000 Integration Questions related to Fractional Brownian Motion Probab. Theory Related Fields 118 251 291 (Pubitemid 33228653)
    • (2000) Probability Theory and Related Fields , vol.118 , Issue.2 , pp. 251-291
    • Pipiras, V.1    Taqqu, M.S.2
  • 32
    • 34548274150 scopus 로고    scopus 로고
    • The 1-d stochastic wave equation driven by a fractional Brownian sheet
    • DOI 10.1016/j.spa.2007.01.009, PII S0304414907000208
    • L. Quer-Sardanyons S. Tindel 2007 The 1-d Stochastic Wave Equation driven by a Fractional Brownian Sheet Stochastic Processes Appl. 117 1448 1472 (Pubitemid 47320968)
    • (2007) Stochastic Processes and their Applications , vol.117 , Issue.10 , pp. 1448-1472
    • Quer-Sardanyons, L.1    Tindel, S.2
  • 33
    • 0031540977 scopus 로고    scopus 로고
    • Arbitrage with Fractional Brownian Motion
    • L.C.G. Roger 1997 Arbitrage with Fractional Brownian Motion Math. Finance 7 95 105
    • (1997) Math. Finance , vol.7 , pp. 95-105
    • Roger, L.C.G.1
  • 34
    • 0037567625 scopus 로고    scopus 로고
    • Equivalence and Hölder-Sobolev regularity of solutions for a class of non-autonomous stochastic partial differential equations
    • DOI 10.1016/S0246-0203(03)00015-3, PII S0246020303000153
    • M. Sanz-Solé P.-A. Vuillermot 2003 Equivalence and Hölder-Sobolev Regularity of Solutions for a Class of Non-Autonomous Stochastic Partial Differential Equations Ann. I. H. Poincaré-PR 39 703 742 (Pubitemid 36678143)
    • (2003) Annales de l'institut Henri Poincare (B) Probability and Statistics , vol.39 , Issue.4 , pp. 703-742
    • Sanz-Sole, M.1    Vuillermot, P.-A.2
  • 36
    • 0242339531 scopus 로고    scopus 로고
    • Stochastic evolution equations with fractional Brownian motion
    • DOI 10.1007/s00440-003-0282-2
    • S. Tindel C.A. Tudor F. Viens 2003 Stochastic Evolution Equations with Fractional Brownian Motion Probab. Theory Related Fields 127 186 204 (Pubitemid 37364575)
    • (2003) Probability Theory and Related Fields , vol.127 , Issue.2 , pp. 186-204
    • Tindel, S.1    Tudor, C.A.2    Viens, F.3
  • 37
    • 0038290919 scopus 로고    scopus 로고
    • Integration with respect to Fractal Functions and Stochastic Calculus i
    • M. Zähle 1998 Integration with respect to Fractal Functions and Stochastic Calculus I Probab. Theory Related Fields 111 333 374
    • (1998) Probab. Theory Related Fields , vol.111 , pp. 333-374
    • Zähle, M.1
  • 38
    • 0041026849 scopus 로고    scopus 로고
    • Integration with respect to fractal functions and stochastic calculus II
    • M. Zähle 2001 Integration with respect to Fractal Functions and Stochastic Calculus II Math. Nachr. 225 145 183 (Pubitemid 33576414)
    • (2001) Mathematische Nachrichten , vol.225 , pp. 145-183
    • Zahle, M.1


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