메뉴 건너뛰기




Volumn 91, Issue 1-2, 1998, Pages 423-438

Scaling limits of solutions of the heat equation for singular non-Gaussian data

Author keywords

Chebyshev Hermite expansions; Heat equation; Long range dependence; Non Gaussian initial conditions; Scaling limit

Indexed keywords


EID: 0032045221     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1023060625577     Document Type: Article
Times cited : (29)

References (30)
  • 1
    • 21844526225 scopus 로고
    • Stratified structure of the Universe and Burgers' equation: A probabilistic approach
    • S. Albeverio, S. A. Molchanov, and D. Surgailis, Stratified structure of the Universe and Burgers' equation: a probabilistic approach, Prob. Theory and Rel. Fields 100:457-484 (1994).
    • (1994) Prob. Theory and Rel. Fields , vol.100 , pp. 457-484
    • Albeverio, S.1    Molchanov, S.A.2    Surgailis, D.3
  • 2
    • 0009140150 scopus 로고
    • Variational formulation of some problems for the random heat equation
    • G. Adomian, ed. Academic Press, New York
    • G. A. Bécus, Variational formulation of some problems for the random heat equation, Applied Stochastic Processes, G. Adomian, ed. (Academic Press, New York, 1980), pp. 19-36.
    • (1980) Applied Stochastic Processes , pp. 19-36
    • Bécus, G.A.1
  • 3
    • 0040634160 scopus 로고
    • High level sojourns for strongly dependent Gaussian processes
    • S. Berman, High level sojourns for strongly dependent Gaussian processes, Z. Wahrschein. verw. Gebiete 50:223-236 (1979).
    • (1979) Z. Wahrschein. Verw. Gebiete , vol.50 , pp. 223-236
    • Berman, S.1
  • 5
    • 0000323474 scopus 로고
    • Central limit theorem for non-linear functional of Gaussian fields
    • P. Breuer and P. Major, Central limit theorem for non-linear functional of Gaussian fields, J. Multivariate Anal. 13:425-441 (1983).
    • (1983) J. Multivariate Anal. , vol.13 , pp. 425-441
    • Breuer, P.1    Major, P.2
  • 6
    • 0000800718 scopus 로고
    • Asymptotic Gaussianness of solutions of the Burgers eqaution with random initial data
    • A. V. Bulinskii and S. A. Molchanov, Asymptotic Gaussianness of solutions of the Burgers eqaution with random initial data, Theory Prob. Appl. 36:217-235 (1991).
    • (1991) Theory Prob. Appl. , vol.36 , pp. 217-235
    • Bulinskii, A.V.1    Molchanov, S.A.2
  • 7
    • 21844495163 scopus 로고
    • Stationary parabolic Anderson model and intermittences
    • R. A. Carmona and S. A. Molchanov, Stationary parabolic Anderson model and intermittences, Probab. Th. Related Fields 102:433-453 (1995).
    • (1995) Probab. Th. Related Fields , vol.102 , pp. 433-453
    • Carmona, R.A.1    Molchanov, S.A.2
  • 8
    • 0002029613 scopus 로고
    • Gaussian and their subordinated self-similar random generalized fields
    • R. L. Dobrushin, Gaussian and their subordinated self-similar random generalized fields, Ann. Prob. 7:1-28 (1979).
    • (1979) Ann. Prob. , vol.7 , pp. 1-28
    • Dobrushin, R.L.1
  • 9
    • 13844294706 scopus 로고
    • Non-central limit theorems for nonlinear functionals of Gaussian fields
    • R. L. Dobrushin and P. Major. Non-central limit theorems for nonlinear functionals of Gaussian fields, Z. Wahr. rerw. Gebiete 50:1-28 (1979).
    • (1979) Z. Wahr. Rerw. Gebiete , vol.50 , pp. 1-28
    • Dobrushin, R.L.1    Major, P.2
  • 10
  • 12
    • 0010667049 scopus 로고
    • An extremal rearrangement property of statisitcal solutions of the Burgers equation
    • Y. Hu and W. A. Woyczynski. An extremal rearrangement property of statisitcal solutions of the Burgers equation, Ann. Appl. Probab. 4:838-858 (1994).
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 838-858
    • Hu, Y.1    Woyczynski, W.A.2
  • 14
    • 0001051311 scopus 로고
    • Random solutions of the partial differential equations
    • University of California Press, Berkeley, California
    • J. Kampé de Feriet, Random solutions of the partial differential equations, Proc. 3rd Berkeley Symp. Math. Stat. Prob. (University of California Press, Berkeley, California, 1955), Vol. III, pp. 199-208.
    • (1955) Proc. 3rd Berkeley Symp. Math. Stat. Prob. , vol.3 , pp. 199-208
    • Kampé De Feriet, J.1
  • 16
    • 34249925120 scopus 로고
    • Tauberian and Abelian theorems for correlation function of homogeneous isotropic random fields
    • N. N. Leonenko and A. Ya. Olenko. Tauberian and Abelian theorems for correlation function of homogeneous isotropic random fields, Ukrainian Math. J. 43:1652-1664 (1991).
    • (1991) Ukrainian Math. J. , vol.43 , pp. 1652-1664
    • Leonenko, N.N.1    Olenko, A.Ya.2
  • 17
    • 0009042242 scopus 로고
    • Limit theorem for solutions of multidimensional Burgers' equation with weak dependent random initial conditions
    • N. N. Leonenko and I. I. Deriev, Limit theorem for solutions of multidimensional Burgers' equation with weak dependent random initial conditions. Theory Prob. and Mathem. Stat. 51:103-115 (1994).
    • (1994) Theory Prob. and Mathem. Stat. , vol.51 , pp. 103-115
    • Leonenko, N.N.1    Deriev, I.I.2
  • 18
    • 0000229756 scopus 로고
    • Limit theorems for solutions of Burgers equation with Gaussian and non-Gaussian initial data
    • N. N. Leonenko and E. Orsingher, Limit theorems for solutions of Burgers equation with Gaussian and non-Gaussian initial data, Theory Prob. Appl. 40:387-336 (1995).
    • (1995) Theory Prob. Appl. , vol.40 , pp. 387-1336
    • Leonenko, N.N.1    Orsingher, E.2
  • 22
    • 38249022603 scopus 로고
    • Generalized Brownian functionals and the solution to a stochastic partial differential equation
    • D. Nualart and M. Zakai, Generalized Brownian functionals and the solution to a stochastic partial differential equation, J. Func. Anal. 84:279-296 (1989).
    • (1989) J. Func. Anal. , vol.84 , pp. 279-296
    • Nualart, D.1    Zakai, M.2
  • 23
    • 0000339717 scopus 로고
    • Remark on the Burgers equation
    • M. Rosenblatt, Remark on the Burgers equation, J. Math. Phys. 9:1129-1136 (1968).
    • (1968) J. Math. Phys. , vol.9 , pp. 1129-1136
    • Rosenblatt, M.1
  • 24
    • 0000609479 scopus 로고
    • Independence and dependence
    • University of California Press, Berkeley
    • M. Rosenblatt, Independence and dependence. Proc. 4th Berkeley Symp. Math. Stat. Prohah. (University of California Press, Berkeley, 1961), pp. 411-443.
    • (1961) Proc. 4th Berkeley Symp. Math. Stat. Prohah. , pp. 411-443
    • Rosenblatt, M.1
  • 25
    • 0000814254 scopus 로고
    • Stabilization of the statistical solutions of the parabolic equation
    • N. E. Rotanov, A. G. Shuhov, and Yu. M. Suhov, Stabilization of the statistical solutions of the parabolic equation, Acta Appl. Math. 22:103-115 (1991).
    • (1991) Acta Appl. Math. , vol.22 , pp. 103-115
    • Rotanov, N.E.1    Shuhov, A.G.2    Suhov, Yu.M.3
  • 26
    • 0002010564 scopus 로고
    • Scaling limits of solutions of the Burgers equation with singular Gaussian initial data
    • C. Houdré and V. Pèrez-Abreu. eds. CRC Press, Boca Raton, FL
    • D. Surgailis and W. A. Woyczynski, Scaling limits of solutions of the Burgers equation with singular Gaussian initial data, in Chaos Expansions, Multiple Wiener-Itô Integrals and Their Applications. C. Houdré and V. Pèrez-Abreu. eds. (CRC Press, Boca Raton, FL, 1994).
    • (1994) Chaos Expansions, Multiple Wiener-Itô Integrals and Their Applications
    • Surgailis, D.1    Woyczynski, W.A.2
  • 27
    • 34250409798 scopus 로고
    • Weak convergence to fractional Brownian motion and to the Rosenblatt process
    • M. S. Taqqu, Weak convergence to fractional Brownian motion and to the Rosenblatt process, Z. Wahrschein. verw. Gebiete 31:287-302 (1975).
    • (1975) Z. Wahrschein. Verw. Gebiete , vol.31 , pp. 287-302
    • Taqqu, M.S.1
  • 28
    • 0001915941 scopus 로고
    • Convergence of integrated precesses of arbitrary Hermite rank
    • M. S. Taqqu, Convergence of integrated precesses of arbitrary Hermite rank, Z. Wahr. verw. gebiete 50:351-362 (1979).
    • (1979) Z. Wahr. Verw. Gebiete , vol.50 , pp. 351-362
    • Taqqu, M.S.1
  • 29
    • 0009223645 scopus 로고
    • A stability properly of the stochastic heat equation
    • J. Ubøe and T. Zhang, A stability properly of the stochastic heat equation, Stoch. Proc. Appl. 60:247-260 (1995).
    • (1995) Stoch. Proc. Appl. , vol.60 , pp. 247-260
    • Ubøe, J.1    Zhang, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.