메뉴 건너뛰기




Volumn 112, Issue 1, 2009, Pages 41-64

Pathwise approximation of stochastic differential equations on domains: Higher order convergence rates without global Lipschitz coefficients

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84894226734     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-008-0200-8     Document Type: Article
Times cited : (57)

References (25)
  • 1
    • 34547536758 scopus 로고    scopus 로고
    • On the discretization schemes for the CIR (and Bessel squared) processes
    • Alfonsi, A.: On the discretization schemes for the CIR (and Bessel squared) processes. Monte Carlo Methods Appl. 11, 355-384 (2005).
    • (2005) Monte Carlo Methods Appl , vol.11 , pp. 355-384
    • Alfonsi, A.1
  • 5
    • 0032026704 scopus 로고    scopus 로고
    • Convergence of discretized stochastic (interest rate) processeswith stochastic drift term
    • Deelstra, G., Delbaen, F.: Convergence of discretized stochastic (interest rate) processeswith stochastic drift term. Appl. Stoch. Models Data Anal. 14, 77-84 (1998).
    • (1998) Appl. Stoch. Models Data Anal , vol.14 , pp. 77-84
    • Deelstra, G.1    Delbaen, F.2
  • 6
    • 28244487471 scopus 로고    scopus 로고
    • Convergence of schemes for stochastic differential equations
    • Fleury, G.: Convergence of schemes for stochastic differential equations. Prob. Eng. Mech. 21, 35-43 (2005).
    • (2005) Prob. Eng. Mech , vol.21 , pp. 35-43
    • Fleury, G.1
  • 7
    • 0031258411 scopus 로고    scopus 로고
    • Variable step size control in the numerical solution of stochastic differential equations
    • Gaines, J. G., Lyons, T. J.: Variable step size control in the numerical solution of stochastic differential equations. SIAM J. Appl. Math. 57, 1455-1484 (1997).
    • (1997) SIAM J. Appl. Math , vol.57 , pp. 1455-1484
    • Gaines, J.G.1    Lyons, T.J.2
  • 8
    • 0042819717 scopus 로고    scopus 로고
    • Pathwise approximation of random ordinary differential equations
    • Grüne, L., Kloeden, P. E.: Pathwise approximation of random ordinary differential equations. BIT 41, 711-721 (2001).
    • (2001) BIT , vol.41 , pp. 711-721
    • Grüne, L.1    Kloeden, P.E.2
  • 9
    • 0043228001 scopus 로고    scopus 로고
    • A note on Euler's approximations
    • Gyöngy, I.: A note on Euler's approximations. Potential Anal. 8, 205-216 (1998).
    • (1998) Potential Anal , vol.8 , pp. 205-216
    • Gyöngy, I.1
  • 10
    • 33749566186 scopus 로고    scopus 로고
    • Convergence ofMonte Carlo simulations involving the mean-reverting square root process
    • Higham, D. J., Mao, X.: Convergence ofMonte Carlo simulations involving the mean-reverting square root process. J. Comp. Finance 8, 35-61 (2005).
    • (2005) J. Comp. Finance , vol.8 , pp. 35-61
    • Higham, D.J.1    Mao, X.2
  • 11
    • 0012279718 scopus 로고    scopus 로고
    • Strong convergence ofEuler-type methods for nonlinear stochastic differential equations
    • Higham, D. J., Mao, X., Stuart, A. M.: Strong convergence ofEuler-type methods for nonlinear stochastic differential equations. SIAM J. Numer. Anal. 40, 1041-1063 (2002).
    • (2002) SIAM J. Numer. Anal , vol.40 , pp. 1041-1063
    • Higham, D.J.1    Mao, X.2    Stuart, A.M.3
  • 12
    • 0038538861 scopus 로고    scopus 로고
    • Semi-implicit Euler-Maruyama scheme for stiff stochastic equations
    • In: Koerezlioglu, H. (ed.), Boston
    • Hu, Y.: Semi-implicit Euler-Maruyama scheme for stiff stochastic equations. In: Koerezlioglu, H. (ed.) Stochastic Analysis and Related Topics V: The SilvriWorkshop, Progr. Prob. 38, Boston, pp. 183-202 (1996).
    • (1996) Stochastic Analysis and Related Topics V: The SilvriWorkshop, Progr. Prob. , vol.38 , pp. 183-202
    • Hu, Y.1
  • 13
    • 38749099790 scopus 로고    scopus 로고
    • Structure preserving stochastic integration schemes in interest rate derivative modeling
    • Kahl, C., Günther, M., Rossberg, T.: Structure preserving stochastic integration schemes in interest rate derivative modeling. Appl. Numer. Math. 58, 284-295 (2008).
    • (2008) Appl. Numer. Math , vol.58 , pp. 284-295
    • Kahl, C.1    Günther, M.2    Rossberg, T.3
  • 16
    • 36348990331 scopus 로고    scopus 로고
    • The pathwise convergence of approximation schemes for stochastic differential equations
    • Kloeden, P. E., Neuenkirch, A.: The pathwise convergence of approximation schemes for stochastic differential equations. LMS JCM 10, 235-253 (2007).
    • (2007) LMS JCM , vol.10 , pp. 235-253
    • Kloeden, P.E.1    Neuenkirch, A.2
  • 18
    • 34247560632 scopus 로고    scopus 로고
    • An adaptive Euler-Maruyama scheme for SDEs: Convergence and stability
    • Lamba, H., Mattingly, J. C., Stuart, A. M.: An adaptive Euler-Maruyama scheme for SDEs: convergence and stability. IMA J. Numer. Anal. 27, 479-506 (2007).
    • (2007) IMA J. Numer. Anal , vol.27 , pp. 479-506
    • Lamba, H.1    Mattingly, J.C.2    Stuart, A.M.3
  • 20
    • 0242563961 scopus 로고    scopus 로고
    • Environmental Brownian noise suppresses explosions in populations dynamics
    • Mao, X., Marion, G., Renshaw, E.: Environmental Brownian noise suppresses explosions in populations dynamics. Stoch. Process. Apl. 97, 95-110 (2002).
    • (2002) Stoch. Process. Apl , vol.97 , pp. 95-110
    • Mao, X.1    Marion, G.2    Renshaw, E.3
  • 22
    • 33745437716 scopus 로고    scopus 로고
    • Numerical integration of stochastic differential equations with nonglobally Lipschitz coefficients
    • Milstein, G. N., Tretjakov, M. V.: Numerical integration of stochastic differential equations with nonglobally Lipschitz coefficients. SIAM J. Numer. Anal. 43, 1139-1154 (2005).
    • (2005) SIAM J. Numer. Anal , vol.43 , pp. 1139-1154
    • Milstein, G.N.1    Tretjakov, M.V.2
  • 23
    • 40849085475 scopus 로고    scopus 로고
    • Weak approximation of stochastic differential equations and application to derivative pricing
    • Ninomiya, S., Victoir, N.: Weak approximation of stochastic differential equations and application to derivative pricing. Appl. Math. Finance 15, 107-121 (2008).
    • (2008) Appl. Math. Finance , vol.15 , pp. 107-121
    • Ninomiya, S.1    Victoir, N.2
  • 24
    • 0020502923 scopus 로고
    • Résolution trajectorielle et analyse numérique des équations différentielles stochastiques
    • Talay, D.: Résolution trajectorielle et analyse numérique des équations différentielles stochastiques. Stochastics 9, 275-306 (1983).
    • (1983) Stochastics , vol.9 , pp. 275-306
    • Talay, D.1
  • 25
    • 0036630423 scopus 로고    scopus 로고
    • The Euler scheme with irregular coefficients
    • Yan, L.: The Euler scheme with irregular coefficients. Ann. Probab. 30, 1172-1194 (2002).
    • (2002) Ann. Probab , vol.30 , pp. 1172-1194
    • Yan, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.