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Volumn 47, Issue 1, 2009, Pages 116-130

An analytical-numerical method for fast evaluation of probability densities for transient solutions of nonlinear Itô's stochastic differential equations

Author keywords

Analytical numerical method; Damping matrix; It 's stochastic differential equation; Motion of ship in stochastic sea; Stochastic rolling of ship; Transition probability density

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DAMPING; DIFFERENTIAL EQUATIONS; DISPERSIONS; ELECTRON ENERGY LEVELS; EQUATIONS OF MOTION; FLOW PATTERNS; MARINE ENGINEERING; MEASUREMENT THEORY; NONLINEAR EQUATIONS; NUMBER THEORY; NUMERICAL METHODS; POLYNOMIAL APPROXIMATION; PROBABILITY; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; SETTLING TANKS; SHIPS; STOCHASTIC CONTROL SYSTEMS; WATER WAVES;

EID: 57649095383     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2008.08.001     Document Type: Article
Times cited : (16)

References (29)
  • 1
    • 57649104456 scopus 로고    scopus 로고
    • R.Z. Has'minskiǐ, Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 1980.
    • R.Z. Has'minskiǐ, Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 1980.
  • 4
    • 7544239423 scopus 로고    scopus 로고
    • Stability and capsizing of ships in random sea - a survey
    • Arnold L., Chueshov I., and Ochs G. Stability and capsizing of ships in random sea - a survey. Nonlinear Dynam. 36 (2004) 135-179
    • (2004) Nonlinear Dynam. , vol.36 , pp. 135-179
    • Arnold, L.1    Chueshov, I.2    Ochs, G.3
  • 5
    • 0347303241 scopus 로고    scopus 로고
    • The nonlinear dynamics of ship motions: a field overview and some recent developments
    • Spyrou K.J., and Thomson J.M.T. The nonlinear dynamics of ship motions: a field overview and some recent developments. R. Soc. Lond. Philos. Trans. Ser. A, Math. Phys. Eng. Sci. 358 1771 (2000) 1735-1760
    • (2000) R. Soc. Lond. Philos. Trans. Ser. A, Math. Phys. Eng. Sci. , vol.358 , Issue.1771 , pp. 1735-1760
    • Spyrou, K.J.1    Thomson, J.M.T.2
  • 6
    • 0346041884 scopus 로고    scopus 로고
    • Markov modelling and stochastic identification for nonlinear ship rolling in random waves
    • Roberts J.B., and Vasta M. Markov modelling and stochastic identification for nonlinear ship rolling in random waves. R. Soc. Lond. Philos. Trans. Ser. A, Math. Phys. Eng. Sci. 358 1771 (2000) 1917-1941
    • (2000) R. Soc. Lond. Philos. Trans. Ser. A, Math. Phys. Eng. Sci. , vol.358 , Issue.1771 , pp. 1917-1941
    • Roberts, J.B.1    Vasta, M.2
  • 7
    • 0030813726 scopus 로고    scopus 로고
    • Isotropic and anisotropic correlations in turbulent wind speed data
    • Henjes K. Isotropic and anisotropic correlations in turbulent wind speed data. Bound.-Lay. Meteorol. 84 1 (1997) 149-167
    • (1997) Bound.-Lay. Meteorol. , vol.84 , Issue.1 , pp. 149-167
    • Henjes, K.1
  • 8
    • 57649106768 scopus 로고
    • Simulation program for maneuverability of ship and its application
    • (in Japanese)
    • Mori M., Tanaka M., and Mizoguchi S. Simulation program for maneuverability of ship and its application. Ishikawajima-Harima Eng. Rev. 13 5 (1973) 571-582 (in Japanese)
    • (1973) Ishikawajima-Harima Eng. Rev. , vol.13 , Issue.5 , pp. 571-582
    • Mori, M.1    Tanaka, M.2    Mizoguchi, S.3
  • 9
    • 23844464156 scopus 로고    scopus 로고
    • M. Minoura, S. Naito, A stochastic model for evaluation of seakeeping performance, in: Proceedings of 14th International Offshore Polar Engineering Conference, 2004 (Int. Soc. of Offshore and Polar Engineers), 2004, pp. 331-338.
    • M. Minoura, S. Naito, A stochastic model for evaluation of seakeeping performance, in: Proceedings of 14th International Offshore Polar Engineering Conference, 2004 (Int. Soc. of Offshore and Polar Engineers), 2004, pp. 331-338.
  • 10
    • 0942277461 scopus 로고    scopus 로고
    • M. Minoura, S. Naito, Modelling of the joint probability of significant wave height and mean wave period, in: Proceedings of 13th International Offshore Polar Engineering Conference, 2003 (Int. Soc. of Offshore and Polar Engineers), 2003, pp. 1383-1390.
    • M. Minoura, S. Naito, Modelling of the joint probability of significant wave height and mean wave period, in: Proceedings of 13th International Offshore Polar Engineering Conference, 2003 (Int. Soc. of Offshore and Polar Engineers), 2003, pp. 1383-1390.
  • 11
    • 0029394467 scopus 로고
    • The solution of the nonlinear Boltzmann equation: a survey of analytic and computational methods
    • Bellomo N., LeTallec P., and Perthame B. The solution of the nonlinear Boltzmann equation: a survey of analytic and computational methods. Comput. Math. Appl. 30 7 (1995) 21-30
    • (1995) Comput. Math. Appl. , vol.30 , Issue.7 , pp. 21-30
    • Bellomo, N.1    LeTallec, P.2    Perthame, B.3
  • 12
    • 0001939954 scopus 로고
    • Stochastic partial differential equations in continuum physics - on the foundations of the stochastic interpolation method for Itô's type equations
    • Bellomo N., and Flandoli F. Stochastic partial differential equations in continuum physics - on the foundations of the stochastic interpolation method for Itô's type equations. Math. Comput. Simulat. 31 1-2 (1989) 3-17
    • (1989) Math. Comput. Simulat. , vol.31 , Issue.1-2 , pp. 3-17
    • Bellomo, N.1    Flandoli, F.2
  • 13
    • 57649094156 scopus 로고    scopus 로고
    • World Scientific, River Edge (NJ, USA) xx+297 pp
    • Mamontov Y.V., and Willander M. High-Dimensional Nonlinear Diffusion Stochastic Processes. Modelling for Engineering Applications. Series on Advances in Mathematics for Applied Sciences. vol. 56 (2001), World Scientific, River Edge (NJ, USA) xx+297 pp
    • (2001) vol. 56
    • Mamontov, Y.V.1    Willander, M.2
  • 14
    • 33746069282 scopus 로고    scopus 로고
    • Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems
    • Bellomo N., and Forni G. Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems. Math. Models Methods Appl. Sci. 16 7 (2006) 1001-1029
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.7 , pp. 1001-1029
    • Bellomo, N.1    Forni, G.2
  • 15
    • 57649096033 scopus 로고    scopus 로고
    • N. Bellomo, Modeling Complex Living Systems. A Kinetic Theory and Stochastic Game Approach, Birkhäuser, Boston, 2007.
    • N. Bellomo, Modeling Complex Living Systems. A Kinetic Theory and Stochastic Game Approach, Birkhäuser, Boston, 2007.
  • 16
    • 57649106128 scopus 로고    scopus 로고
    • E. Dean, R. Glowinski, C.H. Li, Numerical solution of parabolic problems in high dimensions, in: Transactions of 5th Army Conference on Applied Mathematics and Computing, (ARO Rep. 88-01), US Army Res. Office, Research Triangle Park, USA, 1988, pp. 207-285.
    • E. Dean, R. Glowinski, C.H. Li, Numerical solution of parabolic problems in high dimensions, in: Transactions of 5th Army Conference on Applied Mathematics and Computing, (ARO Rep. 88-01), US Army Res. Office, Research Triangle Park, USA, 1988, pp. 207-285.
  • 17
    • 0027226628 scopus 로고
    • Response statistics of nonlinear, compliant offshore structures by the path integral solution method
    • Naess A., and Johnsen J.M. Response statistics of nonlinear, compliant offshore structures by the path integral solution method. Probab. Eng. Mech. 8 (1993) 91-106
    • (1993) Probab. Eng. Mech. , vol.8 , pp. 91-106
    • Naess, A.1    Johnsen, J.M.2
  • 18
    • 0033874591 scopus 로고    scopus 로고
    • Efficient path integration methods for nonlinear dynamic systems
    • Naess A., and Moe V. Efficient path integration methods for nonlinear dynamic systems. Probab. Eng. Mech. 15 (2000) 221-231
    • (2000) Probab. Eng. Mech. , vol.15 , pp. 221-231
    • Naess, A.1    Moe, V.2
  • 19
    • 33745863500 scopus 로고    scopus 로고
    • Response probability density functions of strongly nonlinear systems by the path integration method
    • Iourtchenko D., Mo E., and Naess A. Response probability density functions of strongly nonlinear systems by the path integration method. Int. J. Non-Linear Mech. 41 5 (2006) 693-705
    • (2006) Int. J. Non-Linear Mech. , vol.41 , Issue.5 , pp. 693-705
    • Iourtchenko, D.1    Mo, E.2    Naess, A.3
  • 20
    • 33947215075 scopus 로고    scopus 로고
    • Stochastic spur gear dynamics by numerical path integration
    • Naess A., Kolnes F.E., and Mo E. Stochastic spur gear dynamics by numerical path integration. J. Sound Vib. 302 4-5 (2007) 936-950
    • (2007) J. Sound Vib. , vol.302 , Issue.4-5 , pp. 936-950
    • Naess, A.1    Kolnes, F.E.2    Mo, E.3
  • 21
    • 33745853085 scopus 로고    scopus 로고
    • The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis
    • Mamontov E., Koptioug A.V., and Psiuk-Maksymowicz K. The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis. Acta Biotheor. 54 2 (2006) 61-101
    • (2006) Acta Biotheor. , vol.54 , Issue.2 , pp. 61-101
    • Mamontov, E.1    Koptioug, A.V.2    Psiuk-Maksymowicz, K.3
  • 22
    • 38849109350 scopus 로고    scopus 로고
    • Homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiotherapy
    • Psiuk-Maksymowicz K., and Mamontov E. Homeorhesis-based modelling and fast numerical analysis for oncogenic hyperplasia under radiotherapy. Math. Comput. Modell. 47 5-6 (2008) 580-596
    • (2008) Math. Comput. Modell. , vol.47 , Issue.5-6 , pp. 580-596
    • Psiuk-Maksymowicz, K.1    Mamontov, E.2
  • 23
    • 40149108185 scopus 로고    scopus 로고
    • Dynamic-equilibrium solutions of ordinary differential equations and their role in applied problems
    • Mamontov E. Dynamic-equilibrium solutions of ordinary differential equations and their role in applied problems. Appl. Math. Lett. 21 4 (2008) 320-325
    • (2008) Appl. Math. Lett. , vol.21 , Issue.4 , pp. 320-325
    • Mamontov, E.1
  • 24
    • 20444497719 scopus 로고    scopus 로고
    • Nonstationary invariant distributions and the hydrodynamic-style generalization of the Kolmogorov-forward/Fokker-Planck equation
    • Mamontov E. Nonstationary invariant distributions and the hydrodynamic-style generalization of the Kolmogorov-forward/Fokker-Planck equation. Appl. Math. Lett. 18 9 (2005) 976-982
    • (2005) Appl. Math. Lett. , vol.18 , Issue.9 , pp. 976-982
    • Mamontov, E.1
  • 25
    • 0000189685 scopus 로고
    • Über die analytischen Methoden in der Wahrscheinlichkeit-srechnung
    • Kolmogoroff A. Über die analytischen Methoden in der Wahrscheinlichkeit-srechnung. Math. Ann. 104 1 (1931) 415-458
    • (1931) Math. Ann. , vol.104 , Issue.1 , pp. 415-458
    • Kolmogoroff, A.1
  • 26
    • 84966207705 scopus 로고
    • Diffusion process in one dimension
    • Feller W. Diffusion process in one dimension. Trans. Am. Math. Soc. 77 (1954) 1-31
    • (1954) Trans. Am. Math. Soc. , vol.77 , pp. 1-31
    • Feller, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.