메뉴 건너뛰기




Volumn 41, Issue 1, 2013, Pages 109-133

Functional itô calculus and stochastic integral representation of martingales

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84874965188     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AOP721     Document Type: Article
Times cited : (248)

References (31)
  • 1
    • 0031492385 scopus 로고    scopus 로고
    • Semimartingale integral representation
    • MR1434134
    • AHN, H. (1997). Semimartingale integral representation. Ann. Probab. 25 997-1010. MR1434134
    • (1997) Ann. Probab. , vol.25 , pp. 997-1010
    • Ahn, H.1
  • 2
    • 0011612497 scopus 로고
    • A generalized formula of Itô and some other properties of stochastic flows
    • MR0608026
    • BISMUT, J.-M. (1981). A generalized formula of Itô and some other properties of stochastic flows. Z. Wahrsch. Verw. Gebiete 55 331-350. MR0608026
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.55 , pp. 331-350
    • Bismut, J.-M.1
  • 3
    • 0000450260 scopus 로고
    • Calcul des variations stochastique et processus de sauts
    • MR0701527
    • BISMUT, J.-M. (1983). Calcul des variations stochastique et processus de sauts. Z. Wahrsch. Verw. Gebiete 63 147-235. MR0701527
    • (1983) Z. Wahrsch. Verw. Gebiete , vol.63 , pp. 147-235
    • Bismut, J.-M.1
  • 4
    • 0000855448 scopus 로고
    • The representation of functionals of Brownian motion by stochastic integrals
    • MR0270448
    • CLARK, J. M. C. (1970). The representation of functionals of Brownian motion by stochastic integrals. Ann. Math. Statist. 41 1282-1295. MR0270448
    • (1970) Ann. Math. Statist. , vol.41 , pp. 1282-1295
    • Clark, J.M.C.1
  • 5
    • 74249122962 scopus 로고    scopus 로고
    • A functional extension of the Ito formula
    • MR2586744
    • CONT, R. and FOURNIE, D. (2010). A functional extension of the Ito formula. C. R. Math. Acad. Sci. Paris 348 57-61. MR2586744
    • (2010) C. R. Math. Acad. Sci. Paris , vol.348 , pp. 57-61
    • Cont, R.1    Fournie, D.2
  • 6
    • 77952953212 scopus 로고    scopus 로고
    • Change of variable formulas for nonanticipative functionals on path space
    • MR2652181
    • CONT, R. and FOURNIÉ, D.-A. (2010). Change of variable formulas for nonanticipative functionals on path space. J. Funct. Anal. 259 1043-1072. MR2652181
    • (2010) J. Funct. Anal. , vol.259 , pp. 1043-1072
    • Cont, R.1    Fournié, D.-A.2
  • 7
    • 84971790020 scopus 로고
    • Functionals of diffusion processes as stochastic integrals
    • MR0549305
    • DAVIS, M. H. A. (1980). Functionals of diffusion processes as stochastic integrals. Math. Proc. Cambridge Philos. Soc. 87 157-166. MR0549305
    • (1980) Math. Proc. Cambridge Philos. Soc. , vol.87 , pp. 157-166
    • Davis, M.H.A.1
  • 10
    • 84874974189 scopus 로고    scopus 로고
    • A new approach to the martingale representation theorem
    • MR2569262
    • FITZSIMMONS, P. J. and RAJEEV, B. (2009). A new approach to the martingale representation theorem. Stochastics 81 467-476. MR2569262
    • (2009) Stochastics , vol.81 , pp. 467-476
    • Fitzsimmons, P.J.1    Rajeev, B.2
  • 12
    • 52649154664 scopus 로고
    • Functionals of Itô processes as stochastic integrals
    • MR0474497
    • HAUSSMANN, U. G. (1978). Functionals of Itô processes as stochastic integrals. SIAM J. Control Optim. 16 252-269. MR0474497
    • (1978) SIAM J. Control Optim. , vol.16 , pp. 252-269
    • Haussmann, U.G.1
  • 13
    • 0037978348 scopus 로고
    • On the integral representation of functionals of Itô processes
    • MR0546697
    • HAUSSMANN, U. G. (1979). On the integral representation of functionals of Itô processes. Stochastics 3 17-27. MR0546697
    • (1979) Stochastics , vol.3 , pp. 17-27
    • Haussmann, U.G.1
  • 14
    • 0001455484 scopus 로고
    • Stochastic integral
    • MR0014633
    • ITÔ, K. (1944). Stochastic integral. Proc. Imp. Acad. Tokyo 20 519-524. MR0014633
    • (1944) Proc. Imp. Acad. Tokyo , vol.20 , pp. 519-524
    • Itô, K.1
  • 15
    • 0039769080 scopus 로고
    • On stochastic differential equations
    • ITÔ, K. (1946). On stochastic differential equations. Proc. Imp. Acad. Tokyo 22 32-35.
    • (1946) Proc. Imp. Acad. Tokyo , vol.22 , pp. 32-35
    • Itô, K.1
  • 16
    • 0039771995 scopus 로고    scopus 로고
    • Explicit form and robustness of martingale representations
    • MR1813842
    • JACOD, J.,MÉLÉARD, S. and PROTTER, P. (2000). Explicit form and robustness of martingale representations. Ann. Probab. 28 1747-1780. MR1813842
    • (2000) Ann. Probab. , vol.28 , pp. 1747-1780
    • Jacod, J.1    Méléard, S.2    Protter, P.3
  • 18
    • 84972538901 scopus 로고
    • On square integrable martingales
    • MR0217856
    • KUNITA, H. and WATANABE, S. (1967). On square integrable martingales. Nagoya Math. J. 30 209-245. MR0217856
    • (1967) Nagoya Math. J. , vol.30 , pp. 209-245
    • Kunita, H.1    Watanabe, S.2
  • 19
    • 0032347402 scopus 로고    scopus 로고
    • Differential equations driven by rough signals
    • MR1654527
    • LYONS, T. J. (1998). Differential equations driven by rough signals. Rev. Mat. Iberoam. 14 215-310. MR1654527
    • (1998) Rev. Mat. Iberoam. , vol.14 , pp. 215-310
    • Lyons, T.J.1
  • 22
    • 0001339314 scopus 로고
    • Un cours sur les intégrales stochastiques
    • Univ. Strasbourg, Strasbourg, Année Universitaire 1974/1975). Lecture Notes in Math, Springer, Berlin. MR0501323
    • MEYER, P. A. (1976). Un cours sur les intégrales stochastiques. In Séminaire de Probabilités, X (Seconde Partie: Théorie des Intégrales Stochastiques, Univ. Strasbourg, Strasbourg, Année Universitaire 1974/1975). Lecture Notes in Math. 511 245-400. Springer, Berlin. MR0501332
    • (1976) Séminaire de Probabilités, X (Seconde Partie: Théorie des Intégrales Stochastiques , vol.511 , pp. 245-400
    • Meyer, P.A.1
  • 24
    • 0021443346 scopus 로고
    • Malliavin's calculus and stochastic integral representations of functionals of diffusion processes
    • MR0749372
    • OCONE, D. (1984). Malliavin's calculus and stochastic integral representations of functionals of diffusion processes. Stochastics 12 161-185. MR0749372
    • (1984) Stochastics , vol.12 , pp. 161-185
    • Ocone, D.1
  • 26
    • 33645023909 scopus 로고    scopus 로고
    • Brownian excursions, stochastic integrals, and representation of Wiener functionals
    • (electronic). MR2217815
    • PICARD, J. (2006). Brownian excursions, stochastic integrals, and representation of Wiener functionals. Electron. J. Probab. 11 199-248 (electronic). MR2217815
    • (2006) Electron. J. Probab. , vol.11 , pp. 199-248
    • Picard, J.1
  • 27
    • 33845275169 scopus 로고    scopus 로고
    • Stochastic Integration and Differential Equations, 2nd ed
    • Springer, Berlin. MR2273672
    • PROTTER, P. E. (2005). Stochastic Integration and Differential Equations, 2nd ed. Stochastic Modelling and Applied Probability 21. Springer, Berlin. MR2273672
    • (2005) Stochastic Modelling and Applied Probability 21
    • Protter, P.E.1
  • 29
    • 0001365070 scopus 로고
    • Derivatives of Wiener functionals and absolute continuity of induced measures
    • MR0582167
    • SHIGEKAWA, I. (1980). Derivatives of Wiener functionals and absolute continuity of induced measures. J. Math. Kyoto Univ. 20 263-289. MR0582167
    • (1980) J. Math. Kyoto Univ. , vol.20 , pp. 263-289
    • Shigekawa, I.1
  • 30
    • 0000989873 scopus 로고
    • The Malliavin calculus, a functional analytic approach
    • MR0642917
    • STROOCK, D. W. (1981). The Malliavin calculus, a functional analytic approach. J. Funct. Anal. 44 212-257. MR0642917
    • (1981) J. Funct. Anal. , vol.44 , pp. 212-257
    • Stroock, D.W.1
  • 31
    • 0002638391 scopus 로고
    • Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels
    • MR0877589
    • WATANABE, S. (1987). Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels. Ann. Probab. 15 1-39. MR0877589
    • (1987) Ann. Probab. , vol.15 , pp. 1-39
    • Watanabe, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.