메뉴 건너뛰기




Volumn 6, Issue 2, 2007, Pages 468-492

Self-averaging from lateral diversity in the Itô-Schrödinger equation

Author keywords

Parabolic approximation; Random media; Stochastic partial differential equations

Indexed keywords

BESSEL FUNCTIONS; CORRELATION METHODS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); FUNCTION EVALUATION; MATHEMATICAL TRANSFORMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RANDOM PROCESSES; SOIL MECHANICS; SOIL STRUCTURE INTERACTIONS; TESTING; WAVES;

EID: 38849144031     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/060668882     Document Type: Article
Times cited : (40)

References (29)
  • 1
    • 0030268825 scopus 로고    scopus 로고
    • Parabolic and Gaussian white noise approximation for wave propagation in random media
    • F. BAILLY, J. F. CLOUET, AND J. P. FOUQUE, Parabolic and Gaussian white noise approximation for wave propagation in random media, SIAM J. Appl. Math., 56 (1996), pp. 1445-1470.
    • (1996) SIAM J. Appl. Math , vol.56 , pp. 1445-1470
    • BAILLY, F.1    CLOUET, J.F.2    FOUQUE, J.P.3
  • 2
    • 11244341025 scopus 로고    scopus 로고
    • On the self-averaging of wave energy in random media
    • G. BAL, On the self-averaging of wave energy in random media, Multiscale Model. Simul., 2 (2004), pp. 398-420.
    • (2004) Multiscale Model. Simul , vol.2 , pp. 398-420
    • BAL, G.1
  • 3
    • 0242704793 scopus 로고    scopus 로고
    • G. BAL AND L. RYZHIK, Time reversal and refocusing in random media, SIAM J. Appl. Math., 63 (2003), pp. 1475-1498.
    • G. BAL AND L. RYZHIK, Time reversal and refocusing in random media, SIAM J. Appl. Math., 63 (2003), pp. 1475-1498.
  • 4
    • 0242508288 scopus 로고    scopus 로고
    • Self-averaging of Wigner transforms in random media
    • G. BAL, T. KOMOROWSKI, AND L. RYZHIK, Self-averaging of Wigner transforms in random media, Comm. Math. Phys., 242 (2003), pp. 81-135.
    • (2003) Comm. Math. Phys , vol.242 , pp. 81-135
    • BAL, G.1    KOMOROWSKI, T.2    RYZHIK, L.3
  • 5
    • 0242452121 scopus 로고    scopus 로고
    • Self-averaging in time reversal for the parabolic wave equation
    • G. BAL, G. PAPANICOLAOU, AND L. RYZHIK, Self-averaging in time reversal for the parabolic wave equation, Stoch. Dyn., 2 (2002), pp. 507-531.
    • (2002) Stoch. Dyn , vol.2 , pp. 507-531
    • BAL, G.1    PAPANICOLAOU, G.2    RYZHIK, L.3
  • 6
    • 0042890603 scopus 로고    scopus 로고
    • Radiative transport limit for the random Schrödinger equation
    • G. BAL, G. PAPANICOLAOU, AND L. RYZHIK, Radiative transport limit for the random Schrödinger equation, Nonlinearity, 15 (2002), pp. 513-529.
    • (2002) Nonlinearity , vol.15 , pp. 513-529
    • BAL, G.1    PAPANICOLAOU, G.2    RYZHIK, L.3
  • 8
    • 0017972055 scopus 로고
    • Stability and control of stochastic systems with wide-band noise disturbances
    • G. BLANKENSHIP AND G. C. PAPANICOLAOU, Stability and control of stochastic systems with wide-band noise disturbances. I, SIAM J. Appl. Math., 34 (1978), pp. 437-476.
    • (1978) I, SIAM J. Appl. Math , vol.34 , pp. 437-476
    • BLANKENSHIP, G.1    PAPANICOLAOU, G.C.2
  • 10
    • 23244453191 scopus 로고    scopus 로고
    • Interferometric array imaging in clutter
    • L. BORCEA, G. PAPANICOLAOU, AND C. TSOGKA, Interferometric array imaging in clutter, Inverse Problems, 21 (2005), pp. 1419-1460.
    • (2005) Inverse Problems , vol.21 , pp. 1419-1460
    • BORCEA, L.1    PAPANICOLAOU, G.2    TSOGKA, C.3
  • 11
    • 33746307515 scopus 로고    scopus 로고
    • Adaptive interferometric imaging in clutter and optimal illumination
    • L. BORCEA, G. PAPANICOLAOU, AND C. TSOGKA, Adaptive interferometric imaging in clutter and optimal illumination, Inverse Problems, 22 (2006), pp. 1405-1436.
    • (2006) Inverse Problems , vol.22 , pp. 1405-1436
    • BORCEA, L.1    PAPANICOLAOU, G.2    TSOGKA, C.3
  • 12
    • 45849089294 scopus 로고    scopus 로고
    • Asymptotics for the space-time Wigner transform with applications to imaging, in Stochastic Differential Equations: Theory and Applications
    • L. Rozovskii, P. H. Baxendale and S. V. Lototsky, eds, World Scientific, Singapore, to appear
    • L. BORCEA, G. PAPANICOLAOU, AND C. TSOGKA, Asymptotics for the space-time Wigner transform with applications to imaging, in Stochastic Differential Equations: Theory and Applications. A Volume in Honor of Professor Boris L. Rozovskii, P. H. Baxendale and S. V. Lototsky, eds., World Scientific, Singapore, 2007, to appear.
    • (2007) A Volume in Honor of Professor Boris
    • BORCEA, L.1    PAPANICOLAOU, G.2    TSOGKA, C.3
  • 13
    • 0000850179 scopus 로고    scopus 로고
    • R. BOUC AND E. PARDOUX, A symptotic analysis of PDEs with wide-band noise disturbances and expansion of the moments, Stochastic Anal. Appl., 2 (1984), pp. 369-422.
    • R. BOUC AND E. PARDOUX, A symptotic analysis of PDEs with wide-band noise disturbances and expansion of the moments, Stochastic Anal. Appl., 2 (1984), pp. 369-422.
  • 15
    • 0002275662 scopus 로고
    • Measure-valued Markov processes
    • École d'Été de Probabilités de Saint-Flour XXI, 1991, P. L. Hennequin, ed, Springer-Verlag, Berlin
    • D. A. DAWSON, Measure-valued Markov processes, in École d'Été de Probabilités de Saint-Flour XXI - 1991, P. L. Hennequin, ed., Lecture Notes in Math. 1541, Springer-Verlag, Berlin, 1993, pp. 1-260.
    • (1993) Lecture Notes in Math , vol.1541 , pp. 1-260
    • DAWSON, D.A.1
  • 16
    • 13244281669 scopus 로고    scopus 로고
    • White-noise and geometrical optics limits of Wigner-Moyal equation for wave beams in turbulent media
    • A. FANNJIANG, White-noise and geometrical optics limits of Wigner-Moyal equation for wave beams in turbulent media. Comm. Math. Phys., 254 (2005), pp. 289-322.
    • (2005) Comm. Math. Phys , vol.254 , pp. 289-322
    • FANNJIANG, A.1
  • 17
    • 26044438778 scopus 로고    scopus 로고
    • White-noise and geometrical optics limits of Wigner-Moyal equation for beam waves in turbulent media
    • A. FANNJIANG, White-noise and geometrical optics limits of Wigner-Moyal equation for beam waves in turbulent media. II. Two-frequency formulation. J. Stat. Phys., 120 (2005), pp. 543-586.
    • (2005) II. Two-frequency formulation. J. Stat. Phys , vol.120 , pp. 543-586
    • FANNJIANG, A.1
  • 18
    • 0041500536 scopus 로고
    • La convergence en loi pour les processus à valeurs dans un espace nucléaire
    • J. P. FOUQUE, La convergence en loi pour les processus à valeurs dans un espace nucléaire, Ann. Inst. H. Poincaré Probab. Statist., 20 (1984), pp. 225-245.
    • (1984) Ann. Inst. H. Poincaré Probab. Statist , vol.20 , pp. 225-245
    • FOUQUE, J.P.1
  • 19
    • 0032120856 scopus 로고    scopus 로고
    • Forward and Markov approximation: The strong intensity fluctuations regime revisited
    • J. P. FOUQUE, G. C. PAPANICOLAOU, AND Y. SAMUELIDES, Forward and Markov approximation: The strong intensity fluctuations regime revisited, Waves Random Media, 8 (1998), pp. 303-314.
    • (1998) Waves Random Media , vol.8 , pp. 303-314
    • FOUQUE, J.P.1    PAPANICOLAOU, G.C.2    SAMUELIDES, Y.3
  • 22
    • 0003861445 scopus 로고
    • Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory
    • MIT Press, Cambridge, MA
    • H. KUSHNER, Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory, MIT Press Ser. Signal Process. Optim. Control 6, MIT Press, Cambridge, MA, 1984.
    • (1984) MIT Press Ser. Signal Process. Optim. Control , vol.6
    • KUSHNER, H.1
  • 23
    • 0000467039 scopus 로고
    • Tightness of probabilities on C([0, 1]; S′) and D([0, 1]; S′)
    • I. MITOMA, Tightness of probabilities on C([0, 1]; S′) and D([0, 1]; S′), Ann. Probab., 11 (1983); pp. 989-999.
    • (1983) Ann. Probab , vol.11 , pp. 989-999
    • MITOMA, I.1
  • 24
    • 0026139657 scopus 로고    scopus 로고
    • B. NAIR AND B. S. WHITE, High-frequency wave propagation in random media - a unified approach, SIAM J. Appl. Math., 51 (1991), pp. 374-411.
    • B. NAIR AND B. S. WHITE, High-frequency wave propagation in random media - a unified approach, SIAM J. Appl. Math., 51 (1991), pp. 374-411.
  • 25
    • 4544277793 scopus 로고    scopus 로고
    • G. PAPANICOLAOU, L. RYZHIK, AND K. SØLNA, Statistical stability in time reversal, SIAM J. Appl. Math., 64 (2004), pp. 1133-1155.
    • G. PAPANICOLAOU, L. RYZHIK, AND K. SØLNA, Statistical stability in time reversal, SIAM J. Appl. Math., 64 (2004), pp. 1133-1155.
  • 26
    • 0030388835 scopus 로고    scopus 로고
    • Transport equations for elastic and other waves in random media
    • L. RYZHIK, G. PAPANICOLAOU, AND J. B. KELLER, Transport equations for elastic and other waves in random media, Wave Motion, 24 (1996), pp. 327-370.
    • (1996) Wave Motion , vol.24 , pp. 327-370
    • RYZHIK, L.1    PAPANICOLAOU, G.2    KELLER, J.B.3
  • 27
    • 0000978807 scopus 로고
    • The parabolic approximation method
    • Wave Propagation and Underwater Acoustics, Springer-Verlag, Berlin
    • F. TAPPERT, The parabolic approximation method, in Wave Propagation and Underwater Acoustics, Lecture Notes in Phys. 70, Springer-Verlag, Berlin, 1977, pp. 224-287.
    • (1977) Lecture Notes in Phys , vol.70 , pp. 224-287
    • TAPPERT, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.