메뉴 건너뛰기




Volumn 361, Issue 5, 2009, Pages 2689-2718

Rough path analysis via fractional calculus

Author keywords

Convergence rate; Differential equation; Fractional calculus; Integral; Integration by parts; Rough path; Stability; Stochastic differential equation; Wong zakai approximation

Indexed keywords


EID: 70449678769     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-08-04631-X     Document Type: Article
Times cited : (76)

References (18)
  • 1
    • 23244437743 scopus 로고    scopus 로고
    • Semi-martingales and rough paths theory
    • MR2164030 2006i:60042
    • Coutin, L. and Lejay, A. Semi-martingales and rough paths theory. Electron. J. Probab. 10 (2005), 761-785. MR2164030 (2006i:60042)
    • (2005) Electron. J. Probab. , vol.10 , pp. 761-785
    • Coutin, L.1    Lejay, A.2
  • 2
    • 0036002985 scopus 로고    scopus 로고
    • Stochastic analysis, rough path analysis and fractional Brownian motions
    • MR1883719 2003c:60066
    • Coutin, L. and Qian, Z. Stochastic analysis, rough path analysis and fractional Brownian motions. Probab. Theory Related Fields 122 (2002), 108-140. MR1883719 (2003c:60066)
    • (2002) Probab. Theory Related Fields , vol.122 , pp. 108-140
    • Coutin, L.1    Qian, Z.2
  • 3
    • 36849042730 scopus 로고    scopus 로고
    • Continuity of the Itô-map for Hölder rough paths with applications to the support theorem in Hölder norm
    • IMA Vol. Math. Appl., Springer, New York, MR2202036 2007f:60070
    • Friz, P. K. Continuity of the Itô-map for Hölder rough paths with applications to the support theorem in Hölder norm. In: Probability and partial differential equations in modern applied mathematics, 117-135, IMA Vol. Math. Appl., 140, Springer, New York, 2005. MR2202036 (2007f:60070)
    • (2005) Probability and Partial Differential Equations in Modern Applied Mathematics , vol.140 , pp. 117-135
    • Friz, P.K.1
  • 4
    • 19344371593 scopus 로고    scopus 로고
    • Approximations of the Brownian rough path with applications to stochastic analysis
    • MR2144230 2007e:60018
    • Friz, P. and Victoir, N. Approximations of the Brownian rough path with applications to stochastic analysis. Ann. Inst. H. Poincaré 41 (2005), 703-724. MR2144230 (2007e:60018)
    • (2005) Ann. Inst. H. Poincaré , vol.41 , pp. 703-724
    • Friz, P.1    Victoir, N.2
  • 5
    • 4344654665 scopus 로고    scopus 로고
    • Controlling rough paths
    • MR2091358 2005k:60169
    • Gubinelli, M. Controlling rough paths. J. Funct. Anal. 216 (2004), 86-140. MR2091358 (2005k:60169)
    • (2004) J. Funct. Anal. , vol.216 , pp. 86-140
    • Gubinelli, M.1
  • 6
    • 84883642268 scopus 로고    scopus 로고
    • Differential equations driven by Hölder continuous functions of order greater than 1/2
    • Abel symposium, Springer, MR2397797
    • Hu, Y. and Nualart, D. Differential equations driven by Hölder continuous functions of order greater than 1/2. Stochastic analysis and applications, 399-413, Abel symposium 2, Springer, 2007. MR2397797
    • (2007) Stochastic Analysis and Applications , vol.2 , pp. 399-413
    • Hu, Y.1    Nualart, D.2
  • 7
    • 0036887749 scopus 로고    scopus 로고
    • Large deviations and support theorem for diffusion processes via rough paths
    • MR1935127 2003m:60152
    • Ledoux, M., Qian, Z., and Zhang, T. Large deviations and support theorem for diffusion processes via rough paths. Stochastic Process. Appl. 102 (2002), 265-283. MR1935127 (2003m:60152)
    • (2002) Stochastic Process. Appl. , vol.102 , pp. 265-283
    • Ledoux, M.1    Qian, Z.2    Zhang, T.3
  • 8
    • 23244461120 scopus 로고    scopus 로고
    • An introduction to rough paths
    • MR2053040 2005e:60120
    • Lejay, A. An introduction to rough paths. Lecture Notes in Math. 1832 (2003), 1-59. MR2053040 (2005e:60120)
    • (2003) Lecture Notes in Math. , vol.1832 , pp. 1-59
    • Lejay, A.1
  • 9
    • 0000144882 scopus 로고
    • Differential equations driven by rough signals. I. An extension of an inequality of L. C. Young
    • MR1302388 96b:60150
    • Lyons, T. J. Differential equations driven by rough signals. I. An extension of an inequality of L. C. Young. Math. Res. Lett. 1 (1994), 451-464. MR1302388 (96b:60150)
    • (1994) Math. Res. Lett. , vol.1 , pp. 451-464
    • Lyons, T.J.1
  • 10
    • 0032347402 scopus 로고    scopus 로고
    • Differential equations driven by rough signals
    • MR1654527 2000c:60089
    • Lyons, T. J. Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998), 215-310. MR1654527 (2000c:60089)
    • (1998) Rev. Mat. Iberoamericana , vol.14 , pp. 215-310
    • Lyons, T.J.1
  • 11
    • 34247487371 scopus 로고    scopus 로고
    • Differential equations driven by rough paths
    • Springer-Verlag, MR2314753
    • Lyons, T. J., Caruana, M., and Lévy, T. Differential equations driven by rough paths. Lecture Notes in Math. 1908. Springer-Verlag, 2007. MR2314753
    • (2007) Lecture Notes in Math. , vol.1908
    • Lyons, T.J.1    Caruana, M.2    Lévy, T.3
  • 12
    • 0031234681 scopus 로고    scopus 로고
    • Flow equations on spaces of rough paths
    • MR1471102 99b:58241
    • Lyons, T. J. and Qian, Z. Flow equations on spaces of rough paths. J. Funct. Anal. 149 (1997), 135-159. MR1471102 (99b:58241)
    • (1997) J. Funct. Anal. , vol.149 , pp. 135-159
    • Lyons, T.J.1    Qian, Z.2
  • 14
    • 31444454600 scopus 로고    scopus 로고
    • Large deviations for rough paths of the fractional Brownian motion
    • MR2199801 2007e:60027
    • Millet, A. and Sanz-Solé, M. Large deviations for rough paths of the fractional Brownian motion. Ann. Inst. Henri Poincaré 42 (2006), 245-271. MR2199801 (2007e:60027)
    • (2006) Ann. Inst. Henri Poincaré , vol.42 , pp. 245-271
    • Millet, A.1    Sanz-Solé, M.2
  • 15
    • 0038771348 scopus 로고    scopus 로고
    • Differential equations driven by fractional Brownian motion
    • MR1893308 2003f:60105
    • Nualart, D. and Rǎşcanu, A. Differential equations driven by fractional Brownian motion. Collect. Math. 53 (2002), 55-81. MR1893308 (2003f:60105)
    • (2002) Collect. Math. , vol.53 , pp. 55-81
    • Nualart, D.1    Rǎşcanu, A.2
  • 17
    • 0000821514 scopus 로고
    • An inequality of the Hölder type connected with Stieltjes integration
    • MR1555421
    • Young, L. C. An inequality of the Hölder type connected with Stieltjes integration. Acta Math. 67 (1936) 251-282. MR1555421
    • (1936) Acta Math. , vol.67 , pp. 251-282
    • Young, L.C.1
  • 18
    • 0038290919 scopus 로고    scopus 로고
    • Integration with respect to fractal functions and stochastic calculus. I
    • MR1640795 99j:60073
    • Zähle, M. Integration with respect to fractal functions and stochastic calculus. I. Prob. Theory Relat. Fields 111 (1998) 333-374. MR1640795 (99j:60073)
    • (1998) Prob. Theory Relat. Fields , vol.111 , pp. 333-374
    • Zähle, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.