[1] C. W. Gardiner, Stochastic Methods:
A Handbook for the Natural and Social Sciences (Springer, Berlin, 2009).
[2] R. Zwanzig, Memory Effects in Irreversible Thermodynamics, Phys. Rev. 124, 983 (1961).
CrossRef (DOI)
[3] A. V. Mokshin, R. M. Yulmetyev, and P. Hänggi, Simple Measure of Memory for Dynamical Processes Described by a Generalized Langevin Equation, Phys. Rev. Lett. 95, 200601 (2005).
CrossRef (DOI)
[4] R. Balescu, Memory effects in plasma transport theory, Plasma Phys. Controlled Fusion 42,B1(2000).
CrossRef (DOI)
[5] R. Morgado, F. A. Oliveira, G. G. Batrouni, and A. Hansen, Relation between Anomalous and Normal Diffusion in Systems with Memory, Phys. Rev. Lett. 89, 100601 (2002).
CrossRef (DOI)
[6] F. Piazza and S. Lepri, Heat wave propagation in a nonlinear chain, Phys. Rev. B 79, 094306 (2009).
CrossRef (DOI)
[7] M. A. Despósito and A. D. Viñales, Memory effects in the asymptotic diffusive behavior of a classical oscillator described by a generalized Langevin equation, Phys. Rev. E 77, 031123 (2008).
CrossRef (DOI)
[8] F. N. C. Paraan, M. P. Solon, and J. P. Esguerra, Brownian motion of a charged particle driven internally by correlated noise, Phys. Rev. E 77, 022101 (2008).
CrossRef (DOI)
[9] A. J. Majda and P. R. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Phys. Rep. 314, 237 (1999).
CrossRef (DOI)
[10] C. Aslangul, J.-Ph. Bouchaud, A. Georges, N. Pottier, and D. Saint-James, Exact results and self-averaging properties for random-random walks on a one-dimensional infinite lattice, J. Stat. Phys. 55, 461 (1989).
CrossRef (DOI)
[11] J. Eberhard, N. Suciu, and C. Vamoş, On the self-averaging of dispersion for transport in quasi-periodic random media, J. Phys. A: Math. Theor. 40, 597 (2007).
CrossRef (DOI)
[12] J. L. Doob, Stochastic Processes (Wiley, New York, 1990).
[13] P. E. Kloeden and E. Platen, Numerical Solutions of Stochastic Differential Equations (Springer, Berlin, 1999).
[14] J.-P. Bouchaud, A. Georges, J. Koplik, A. Provata, and S. Red-ner, Superdiffusion in random velocity fields, Phys. Rev. Lett. 64, 2503 (1990).
CrossRef (DOI)
[15] J.-P. Bouchaud and A. Georges, Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications, Phys. Rep. 195, 127 (1990).
CrossRef (DOI)
[16] P. Castiglione, Diffusion coefficients as function of Kubo number in random fields, J. Phys. A 33, 1975 (2000).
CrossRef (DOI)
[17] C. L. Zirbel, Lagrangian observations of homogeneous random environments, Adv. Appl. Probab. 33, 810 (2001).
CrossRef (DOI)
[18] N. Suciu, C. Vamoş, H. Vereecken, K. Sabelfeld, and P. Knab-ner, Revue d’Analyse Numérique et de Théorie de l’Approximation 37, 221 (2008).
[19] A. Fannjiang and T. Komorowski, Turbulent diffusion in Markovian flows, Ann. Appl. Probab. 9, 591 (1999).
CrossRef (DOI)
[20] P. K. Kitanidis, Prediction by the method of moments of transport in a heterogeneous formation, J. Hydrol. 102, 453 (1988).
CrossRef (DOI)
[21] N. Suciu, C. Vamoş, H. Vereecken, K. Sabelfeld, and P. Knab-ner, Mathematics Department, Friedrich-Alexander University Erlangen-Nuremberg, Preprint No. 324, 2008, url: http://www.am.uni-erlangen.de/en/prepreprints.2000.html
[22] H. Kesten and G. C. Papanicolaou, A limit theorem for turbulent diffusion, Commun. Math. Phys. 65, 97 (1979).
CrossRef (DOI)
[23] N. Suciu, C. Vamoş, and J. Eberhard, ??title??, Water Resour. Res. 42,W11504 (2006).
[24] N. Suciu (unpublished).
[25] N. Suciu, C. Vamoş, H. Vereecken, K. Sabelfeld, and P. Knab-ner, Water Resour. Res. 44, W08501 (2008).
[26] G. Sposito and G. Dagan, Predicting solute plume evolution in heterogeneous porous formations, Water Resour. Res. 30, 585 (1994) .
CrossRef (DOI)
[27] C. Vamoş,Ş.Şoltuz, and M. Crăciun, e-print arXiv:0709.2963.
[28] N. Suciu and C. Vamoş,in Monte Carlo and QuasiMonteCarlo Methods 2008, edited by P. L’Ecuyer and A. B. Owen(Springer, Heidelberg, to be published).
[29] C. L. Winter, C. M. Newman, and S. P. Neuman, A Perturbation Expansion for Diffusion in a Random Velocity Field, SIAM J.Appl. Math. 44,411(1984).
CrossRef (DOI)
[30] M. G. Trefry, F. P. Ruan, and D. McLaughlin, Water Resour.Res. 39, 1063 (2003).
[31] A. Compte and M. O. Cáceres, Fractional Dynamics in Random Velocity Fields, Phys. Rev. Lett. 81, 3140(1998).
CrossRef (DOI)
[32] C. Vamoş, N. Suciu, and H. Vereecken, Generalized random walk algorithm for the numerical modeling of complex diffusion processes, J. Comput. Phys. 186, 527 (2003).
CrossRef (DOI)
[33] N. Suciu, C. Vamoş, J. Vanderborght, H. Hardelauf, and H.Vereecken, Numerical investigations on ergodicity of solute transport in heterogeneous aquifers, Water Resour. Res. 42, W04409 (2006).
CrossRef (DOI)
[34] P. Le Doussal and J. Machta, Annealed versus quenched diffusion coefficient in random media, Phys. Rev. B 40, 9427 (1989).
CrossRef (DOI)
[35] N. Suciu and C. Vamoş, Comment on “Nonstationary flow and nonergodic transport in random porous media” by G. Darvini and P. Salandin, Water Resour. Res. 43, W12601(2007).
CrossRef (DOI)
[36] A. M. Yaglom, Correlation Theory of Stationary and RelatedRandom Functions, Basic Results Vol. I (Springer, New York,1987).
[37] C. Vamoş, N. Suciu, H. Vereecken, J. Vanderborht, and O.Nitzsche, Forschungszentrum Jülich Report No. ICG-IV.00501, 2001 (unpublished).
[38] S. C. Ying, I. Vattulainen, J. Merikoski, T. Hjelt, and T. Ala-Nissila, Memory expansion for diffusion coefficients, Phys. Rev. B 58, 2170 (1998).
CrossRef (DOI)
[39] N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981)
