1.
Bényi, Á. and Oh, T., Modulation spaces, Wiener amalgam spaces, and Brownian motions, Adv. Math.
228(5) (2011), 2943–2981.

2.
Bourgain, J., Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations II, Geom. Funct. Analysis
3(3) (1993), 209–262.

3.
Bourgain, J., Periodic nonlinear Schrödinger equation and invariant measures, Commun. Math. Phys. 166 (1994), 1–26.

4.
Bourgain, J., On the Cauchy and invariant measure problem for the periodic Zakharov system, Duke Math. J. 76 (1994), 175–202.

5.
Bourgain, J., Invariant measures for the 2D-defocusing nonlinear Schrödinger equation, Commun. Math. Phys. 176(2) (1996), 421–445.

6.
Bourgain, J., Invariant measures for the Gross-Pitaevskii equation, J. Math. Pures Appl. 76(8) (1997), 649–702.

7.
Bourgain, J., Refinements of Strichartz’ inequality and applications to 2D-NLS with critical nonlinearity, Int. Math. Res. Not. 1998(5) (1998), 253–283.

8.
Bourgain, J., Nonlinear Schrödinger equations, in Hyperbolic equations and frequency interactions, IAS/Park City Mathematics Series, Volume 5, pp. 3–157 (American Mathematical Society/IAS/Park City Mathematics Institute, 1999).

9.
Bourgain, J., Invariant measures for NLS in infinite volume, Commun. Math. Phys. 210(3) (2000), 605–620.

10.
Bourgain, J., A remark on normal forms and the ‘I-method’ for periodic NLS, J. Analysis Math.
94 (2004), 125–157.

11.
Burq, N. and Tzvetkov, N., Invariant measure for a three dimensional nonlinear wave equation, Int. Math. Res. Not. 2007(22) (2007), Art. ID rnm108.

12.
Burq, N. and Tzvetkov, N., Random data Cauchy theory for supercritical wave equations, I: local theory, Invent. Math.
173(3) (2008), 449–475.

13.
Burq, N. and Tzvetkov, N., Random data Cauchy theory for supercritical wave equations, II: a global existence result, Invent. Math.
173(3) (2008), 477–496.

14.
Burq, N. and Tzvetkov, N., Probabilistic well-posedness for the cubic wave equation, J. Eur. Math. Soc. 16(1) (2014), 1–30.

15.
Burq, N., Thomann, L. and Tzvetkov, N., Global infinite energy solutions for the cubic wave equation, Bull. Soc. Math. France
143(2) (2015), 301–313.

16.
Cameron, R. and Martin, W., Transformations of Wiener integrals under translations, Annals Math. (2) 45 (1944), 386–396.

17.
Colliander, J. and Oh, T., Almost sure well-posedness of the periodic cubic nonlinear Schrödinger equation below *L*
^{2}(T), Duke Math. J. 161(3) (2012), 367–414.

18.
Prato, G. Da, An introduction to infinite-dimensional analysis, Universitext (Springer, 2006).

19.
Deng, Y., Invariance of the Gibbs measure for the Benjamin–Ono equation, J. Eur. Math. Soc. 17(5) (2015), 1107–1198.

20.
Suzzoni, A.-S. de, Invariant measure for the cubic wave equation on the unit ball of R^{3}
, Dynam. PDEs
8(2) (2011), 127–147.

21.
Suzzoni, A.-S. de, Wave turbulence for the BBM equation: stability of a Gaussian statistics under the flow of BBM, Commun. Math. Phys. 326(3) (2014), 773–813.

22.
Feldman, J., Equivalence and perpendicularity of Gaussian processes, Pac. J. Math.
8 (1958), 699–708.

23.
Freidlin, M. and Wentzell, A., Random perturbations of dynamical systems, 3rd edn, Grundlehren der Mathematischen Wissenschaften, Volume 260 (Springer, 2012).

24.
Gross, L., Abstract Wiener spaces, in Proc. 5th Berkeley Symposium on Mathematical Statistics and Probability, Volume 2, pp. 31–42 (University of California Press, Berkeley, CA, 1965).

25.
Hájek, J., On a property of normal distribution of any stochastic process, Czech. Math. J. 8(83) (1958), 610–618 (in Russian).

26.
Kakutani, S., On equivalence of infinite product measures, Annals Math. (2) 49 (1948). 214–224.

27.
Kappeler, T. and Topalov, P., Global wellposedness of KdV in *H*^{-}
^{1}(,), Duke Math. J. 135(2) (2006), 327–360.
28.
Kuo, H., Gaussian measures in Banach spaces, Lecture Notes in Mathematics, Volume 463 (Springer, 1975).

29. J. Lebowitz, H. Rose and Speer, E., Statistical mechanics of the nonlinear Schrödinger equation, J. Statist. Phys. 50(3) (1988), 657–687.

30.
McKean, H. P., Statistical mechanics of nonlinear wave equations, IV: cubic Schrödinger, Commun. Math. Phys. 168(3) (1995), 479–491 (Erratum, *Commun. Math. Phys*. 173(3) (1995), 675).

31.
Nahmod, A., Oh, T. ,Rey-Bellet, L.and Staffilani, G., Invariant weighted Wiener measures and almost-sure global well-posedness for the periodic derivative NLS, J. Eur. Math. Soc. 14 (2012), 1275–1330.

32.
Nahmod, A., Pavlović, N. and Staffilani, G., Almost sure existence of global weak solutions for super-critical Navier–Stokes equations, SIAM J. Math. Analysis
45(6) (2013), 3431–3452.

33.
Oh, T., Gibbs measures, Invariant and global, a.s.
well-posedness for coupled KdV systems, Diff. Integ. Eqns
22(7–8) (2009), 637–668.

34.
Oh, T., Invariance of the white noise for KdV, Commun. Math. Phys. 292(1) (2009), 217–236.

35.
Oh, T., Periodic stochastic Korteweg-de Vries equation with the additive space-time white noise, Analysis PDEs
2(3) (2009), 281–304.

36.
Oh, T., Invariance of the Gibbs measure for the Schrödinger–Benjamin–Ono system, SIAM J. Math. Analysis
41(6) (2009), 2207–2225.

37.
Oh, T., White noise for KdV and mKdV on the circle, RIMS Kôkyûroku Bessatsu
B18 (2010), 99–124.

38.
Oh, T., Remarks on nonlinear smoothing under randomization for the periodic KdV and the cubic Szegö equation, Funkcial. Ekvac. 54(3) (2011), 335–365.

39.
Oh, T. and Sulem, C., On the one-dimensional cubic nonlinear Schrödinger equation below
L^{2}, Kyoto J. Math.
52(1) (2012), 99–115.

40.
Oh, T., Quastel, J.and Valkó, B., Interpolation of Gibbs measures with white noise for Hamiltonian PDE, J. Math. Pures Appl. 97(4) (2012), 391–410.

41. J. Quastel, B.
Valkó, KdV preserves white noise, Commun. Math. Phys. 277(3) (2008), 707–714.

42.
Richards, G., Invariance of the Gibbs measure for the periodic quartic gKdV, Annales Inst. H. Poincaré Analyse Non Linéaire, in the press.

43.
Shigekawa, I., Stochastic analysis, Translations of Mathematical Monographs, Volume 224 (American Mathematical Society, Providence, RI, 2004).

44.
Tzvetkov, N., Invariant measures for the nonlinear Schrödinger equation on the disc, Dynam. PDEs
3(2) (2006), 111–160.

45.
Tzvetkov, N., Invariant measures for the defocusing nonlinear Schrödinger equation, Annales Inst. Fourier
58 (2008), 2543–2604.

46.
Tzvetkov, N., Construction of a Gibbs measure associated to the periodic Benjamin–Ono equation, Prob. Theory Relat. Fields
146 (2010), 481–514.

47.
Varadhan, S. R. S., Asymptotic probabilities and differential equations, Commun. Pure Appl. Math.
19 (1966), 261–286.