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1997 | 72 | 1 | 147-171
Tytuł artykułu

Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Rocznik
Tom
72
Numer
1
Strony
147-171
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-10-30
poprawiono
1996-05-29
Twórcy
autor
  • Mathematical Institute, Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
autor
  • Department of Mathematics, Faculty of Science, Rua Ernesto de Vasconcelos, Bloco C1, Piso 3, 1700 Lisboa, Portugal
Bibliografia
  • [1] L. Arnold, R. F. Curtain and P. Kotelenez, Nonlinear stochastic evolution equations in Hilbert space, Report no. 17, Forschungsschwerpunkt Dynamische Systeme, Universität Bremen 1980.
  • [2] A. Chojnowska-Michalik and B. Gołdys, Existence, uniqueness and invariant measures for stochastic semilinear equations on Hilbert spaces, Probab. Theory Related Fields 102 (1995), 331-356.
  • [3] G. Da Prato and A. Debussche, Stochastic Cahn-Hilliard equation, preprint Scuola Normale Superiore Pisa no. 5/1994.
  • [4] G. Da Prato, D. Elworthy and J. Zabczyk, Strong Feller property for stochastic semilinear equations, Stochastic Anal. Appl. 13 (1993), 35-45.
  • [5] G. Da Prato and D. Gątarek, Stochastic Burgers equation with correlated noise, Stochastics Stochastics Rep. 52 (1995), 29-41.
  • [6] G. Da Prato, D. Gątarek and J. Zabczyk, Invariant measures for semilinear stochastic equations, Stochastic Anal. Appl. 10 (1992), 387-408.
  • [7] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.
  • [8] G. Da Prato and J. Zabczyk, Non-explosion, boundedness and ergodicity for stochastic semilinear equations, J. Differential Equations 98 (1992), 181-195.
  • [9] F. Flandoli and B. Maslowski, Ergodicity of the 2-D Navier-Stokes equation under random perturbations, Comm. Math. Phys. 171 (1995), 119-141.
  • [10] A. Friedman, Stochastic Differential Equations and Applications, Vol. I, Academic Press, New York, 1975.
  • [11] M. Fuhrman, Densities of Gaussian measures and regularity of non-symmetric Ornstein-Uhlenbeck semigroups in Hilbert spaces, IMPAN, Warszawa, Preprint 528 (1994).
  • [12] D. Fujiwara, Concrete characterization of the domain of fractional powers of some elliptic differential operators of the second order, Proc. Japan Acad. Ser. A Math. Sci. 43 (1967), 82-86.
  • [13] D. Gątarek and B. Gołdys, On solving stochastic equation by the change of drift with application to optimal control, in: Stochastic PDE's and Applications, Proceedings, Pitman, 1992, 180-190.
  • [14] D. Gątarek and B. Gołdys, On invariant measures for diffusions on Banach spaces, Potential Anal., to appear.
  • [15] B. Gołdys, On some regularity properties of solutions to stochastic evolution equations in Hilbert spaces, Colloq. Math. 58 (1990), 327-338.
  • [16] S. Jacquot and G. Royer, Ergodicity of stochastic plates, Probab. Theory Related Fields, submitted.
  • [17] S. Jacquot and G. Royer, Ergodicité d'une classe d'équations aux dérivées partielles stochastiques, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), 231-236.
  • [18] G. Kallianpur, Zero-one laws for Gaussian processes, Trans. Amer. Math. Soc. 149 (1970), 199-211.
  • [19] R. Z. Khas'minskiĭ, Ergodic properties of recurrent diffusion processes and stabilization of the solutions to the Cauchy problem for parabolic equations, Theory Probab. Appl. 5 (1960), 179-196.
  • [20] P. Kotelenez, A maximal inequality for stochastic convolution integrals on Hilbert spaces and space-time regularity of linear stochastic partial differential equations, Stochastics 21 (1987), 345-358.
  • [21] A. Lasota, Statistical stability of deterministic systems, in: Proceedings Würzburg 1982, Lecture Notes in Math. 1017, Springer, Berlin, 1983, 386-419.
  • [22] A. Lasota and M. C. Mackey, Chaos, fractals, and noise, Springer, New York, 1994.
  • [23] A. Lasota and J. A. Yorke, Exact dynamical systems and the Frobenius-Perron operator, Trans. Amer. Math. Soc. 273 (1982), 375-384.
  • [24] G. Leha and G. Ritter, Lyapunov-type conditions for stationary distributions of diffusion processes on Hilbert spaces, Stochastics Stochastics Rep. 48 (1994), 195-225.
  • [25] R. Manthey and B. Maslowski, Qualitative behaviour of solutions of stochastic reaction-diffusion equations, Stochastic Process. Appl. 43 (1992), 265-289.
  • [26] B. Maslowski, On probability distributions of solutions of semilinear stochastic evolution equations, Stochastics Stochastics Rep. 45 (1993), 17-44.
  • [27] B. Maslowski, An application of l-condition in the theory of stochastic differential equations, Časopis Pěst. Mat. 112 (1987), 296-307.
  • [28] B. Maslowski, Strong Feller property for semilinear stochastic evolution equations and applications, in: Proc. Jabłonna 1988, Lecture Notes in Control and Inform. Sci. 136, Springer, Berlin, 1989, 210-225.
  • [29] B. Maslowski and J. Seidler, Ergodic properties of recurrent solutions of stochastic evolution equations, Osaka J. Math. 31 (1994), 965-1003.
  • [30] S. Peszat and J. Zabczyk, Strong Feller property and irreducibility for diffusions on Hilbert spaces, Ann. Probab. 23 (1995), 157-172.
  • [31] J. Seidler, Da Prato-Zabczyk's maximal inequality revisited I, Math. Bohem. 118 (1993), 67-106.
  • [32] J. Seidler, Ergodic behaviour of stochastic parabolic equations, Czechoslovak Math. J., to appear.
  • [33] I. Simão, Regular transition densities for infinite dimensional diffusions, Stochastic Anal. Appl. 11 (1993), 309-336.
  • [34] I. Simão, A conditioned Ornstein-Uhlenbeck process on a Hilbert space, ibid. 9 (1991), 85-98.
  • [35] I. Simão, Pinned Ornstein-Uhlenbeck processes on an infinite dimensional space, Preprint CMAF, University of Lisbon, 1995.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv72i1p147bwm
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