[38] L. Borcea, I. Issa, and C. Tsogka, *Source localization in random acoustic waveguides*, SIAM Multiscale Model. Simul. **5** (2010), 1981–2022.

[39] L. Borcea, G. C. Papanicolaou, and C Tsogka, *Interferometric array imaging in clutter*, Inverse Probl. **21** (2005), 1419–1460.

[40] F. Bouchut, *Hypoelliptic regularity in kinetic equations*, J. Math. Pures Appl. **81** (2002), 1135–1159.

[41] N. Bournaveas and S. Gutiérrez, *On the regularity of averages over spheres for kinetic transport equations in hyperbolic Sobolev spaces*, Rev. Mat. Iberoam. **23** (2007), 481–512.

[42] ——, *Averages over spheres for kinetic transport equations with velocity derivatives in the right-hand side*, SIAM J. Math. Anal. **40** (2008), 653–674.

[43] N. Bournaveas and B. Perthame, *Averages over spheres for kinetic transport equations; hyperbolic Sobolev spaces and Strichartz inequalities*, J. Math. Pures Appl. (9) **80** (2001), 517–534.

[44] N. Bournaveas and H. Wang, *Velocity averaging lemmas in hyperbolic Sobolev spaces for the kinetic transport equation with velocity field on the sphere*, **16** (2009), 131–142.

[45] M. Butz, *Kinetic limit for wave propagation in a continuous, weakly random medium*, Ph.D. thesis, Technische Universität München, 2015.

[46] M Caputo, J. M Carcione, and F Cavallini, *Wave simulation in biologic media based on the kelvin-voigt fractional-derivative stress-strain relation*, Ultrasound in Medicine & Biology **37** (2011), 996–1004.

[47] S. Catheline, T. Gallot, P. Roux, G. Ribay, and J. De Rosny, *Coherent backscattering enhancement in cavities: The simple-shape cavity revisited*, Wave Motion **48** (2011), 214–222.

[48] S. Chandrasekhar, *Radiative transfer*, Dover Publications, New York, 1960.

[49] G. Chen and C. Qiuming, *Fractal density modeling of crustal heterogeneity from the ktb deep hole*, J. Geophys. Res. Solid Earth **122** (2017), 1919–1933.

[50] L. L. Chen, N. Blumm, N. A. Christakis, A. L. Barabasi, and T. S. Deisboeck, *Cancer metastasis networks and the prediction of progression patterns*, Br. J. Cancer **101** (2009), 749–758.

[51] T. Chen, T. Komorovski, and L. Ryzhik, *The weak coupling limit for the random Schrödinger equation: The average wave function*, Arch. Rational Mech. Anal. **227** (2018), 387–422.

[52] J. F. Claerbout, *Imaging the earth's interior*, Blackwell Science, Palo Alto, CA, 1985.

[53] S. Cohen and J. Rosiński, *Gaussian approximation of multivariate lévy processes with applications to simulation of tempered stable processes*, Bernoulli **13** (2007), 195–210.

[54] M. D Collins and W. L Siegmann, *Parabolic equation techniques for seismology, seism-acoustics, and arctic acoustics*, Journal of Theoretical and Computational Acoustics **29** (2021), 2130003.

[55] E. Comen, L. Norton, and J. Massague, *Clinical implications of cancer self-seeding*, Nat. Rev. Clin. Oncol. **8** (2011), 369–377.

[56] H. Contopanagos, B. Dembart, M. Epton, J. J. Ottusch, V. Rokhlin, J.L. Visher, and S.M. Wandzura, *Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering*, IEEE Trans. Antennas Propag. **50** (2002), 1824–1830.

[57] M. Darmon, V. Dorval, and F. Baqué, *Acoustic scattering models from rough surfaces: a brief review and recent advances*, Appl. Sci. **10** (2020), 8305.

[58] D. A. Dawson and G. C. Papanicolaou, *A random wave process*, Appl. Math. Optim. **12** (1984), 97–114.
[59] K. Debrabant and A. Rößer, Families of efficient second order runge-kutta methods for the weak approximation of itô stochastic differential equations, Appl. Numer. Math. **59** (2009), 582–594.

[60] S. Dolan, C. Bean, and B Riotlet, The broad-band fractal nature of heterogeneity in the upper crust from petrophysical logs, Geophys. J. Int. **132** (1998), 489–507.

[61] L. B. Dozier, A numerical treatment of rough surface scattering for the parabolic wave equation, J. Acoust. Soc. Am. **75** (1984), 1415–1432.

[62] F.A. Duck, Physical properties of tissue, Academic Press, London, 1996.

[63] A. I. Dyachenko, E. A. Kuznetsov, M. D. Spector, and V. E. Zakharov, Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping), Phys. Lett. A **221** (1996), 73–79.

[64] L. Erdös, M. Salmhofer, and H.-T. Yau, Quantum diffusion of the random Schrödinger evolution in the scaling limit ii. the recollision diagrams, Comm. Math. Phys. **271** (2007), 1–53.

[65] —, Quantum diffusion of the random Schrödinger evolution in the scaling limit i. the non-recollision diagrams, Acta Math. **200** (2008), 211–277.

[66] L. Erdös and H.-T. Yau, Linear boltzmann equation as the weak coupling limit of the random Schrödinger equation, Commun. Pure Appl. Math. **53** (2000), 667–735.

[67] A. Fannjiang and T. Komorowski, Fractional brownian motions in a limit of turbulent transport, Ann. Appl. Probab. **10** (2000), 1100–1120.

[68] A. C. Fannjiang and K. Sølna, Scaling limits for beam wave propagation in atmospheric turbulence, Stoch. Dyn. **4** (2004), 135–151.

[69] —, Propagation and time-reversal of wave beams in atmospheric turbulence, SIAM Multi-scale Model. Simul. **3** (2005), 522–558.

[70] J.-P. Fouque, J. Garnier, G. C. Papanicolaou, and K. Sølna, Wave propagation and time reversal in randomly layered media, Stochastic Modelling and Applied Probability, vol. 56, Springer, New York, 2007.

[71] M.I. Freidlin and M. Weber, Random perturbations of nonlinear oscillators, Ann. Probab. **26** (1998), 925–967.

[72] M.I. Freidlin and A.D Wentzell, Diffusion processes on graphs and the averaging principle, Ann. Probab. **21** (1993), 2215–2245.

[73] —, Random perturbations of hamiltonian systems, Mem. Amer. Math. Soc. **109** (1994), viii+82.

[74] P. K. Friz and M. Hairer, A course on rough paths: with an introduction to regularity structures, Universitext, Springer Cham, 2014.

[75] M. Fukushima, Dirichlet forms and Markov processes, North-Holland Mathematical Library, vol. 23, North-Holland Publishing Co., Amsterdam-New York; Kodansha, Ltd., Tokyo, 1980.

[76] T. Gallot, S. Catheline, and P. Roux, Coherent backscattering enhancement in cavities. highlights of the role of symmetry, J. Acoust. Soc. Am. **129** (2011), 1963–1971.

[77] A. E. Gargett, The scaling of turbulence in the presence of stable stratification, J. Geophys. Res. **93** (1988), 5021–5036.

[78] J. Garnier, Multi-scaled diffusion-approximation. Applications to wave propagation in random media, ESAIM Probab. Statist. **1** (1997), 183–206.

[79] —, The role of evanescent modes in randomly perturbed single-mode waveguides, Discrete Cont. Dyn.-B **8** (2007), 455–472.
[80] __________, *Ghost imaging in the random paraxial regime*, Inverse Problems and Imaging **10** (2016), 409–432.

[81] J. Garnier, J. C. Munoz Grajales, and A. Nachbin, *Effective behavior of solitary waves over random topography*, SIAM Multiscale Model. Simul. **6** (2007), 995–1025.

[82] J. Garnier and K. Sølna, *Effective transport equations and enhanced backscattering in random waveguides*, SIAM J. Appl. Math **68** (2008), 1574–1599.

[83] __________, *Coupled paraxial wave equations in random media in the white-noise regime*, Ann. Appl. Probab. **19** (2009), 318–346.

[84] __________, *Pulse propagation in random media with long-range correlation*, SIAM Multiscale Model. Simul. **7** (2009), 1302–1324.

[85] __________, *Effective fractional acoustic wave equations in random multiscale media*, J. Acoust. Soc. Am. **127** (2010), 67–72.

[86] __________, *Scintillation in the white-noise paraxial regime*, Commun. Part. Diff. Eq. **39** (2014), 626–650.

[87] __________, *Focusing waves through a randomly scattering medium in the white-noise paraxial regime*, SIAM J. Appl. Math. **77** (2017), 500–519.

[88] __________, *Imaging through a scattering medium by speckle intensity correlations*, Inverse Probl. **34** (2018), 094003.

[89] S. Gelinsky, S. A. Shapiro, and T. Müller, *Dynamic poroelasticity of thinly layered structure*, Int. J. Solids Structures **35** (1998), 4739–4751.

[90] A. Gomez, A. Callejas, G. Rus, and N. Saffari, *Experimental evidence of shear waves in fractional viscoelastic rheological models*, Sci Rep **12** (2022), 7448.

[91] C. Gomez, *Wave propagation in shallow-water acoustic random waveguides*, Commun. Math. Sci. **9** (2011), 81–125.

[92] __________, *Radiative transport limit for the random Schrödinger equation with long-range correlations*, J. Math. Pures Appl. **98** (2012), 295–327.

[93] __________, *Wave decoherence for the random Schrödinger equation with long-range correlations*, Commun. Math. Phys. **320** (2013), 37–71.

[94] __________, *Wave propagation in underwater acoustic waveguides with rough boundaries*, Commun. Math. Sci. **13** (2015), 2005–2052.

[95] C. Gomez and O. Pinaud, *Fractional white-noise limit and paraxial approximation for waves in random media*, Arch. Rational Mech. Anal. **226** (2017), 1061–1138.

[96] __________, *Monte carlo methods for radiative transfer with singular kernels*, SIAM J. Sci. Comput. **40** (2018), A1714–A1741.

[97] C. Gomez, O. Pinaud, and L. Ryzhik, *Hypoelliptic estimates in radiative transfer*, Commun. Part. Diff. Eq. **41** (2015), 150–184.

[98] __________, *Radiative transfer with long-range interactions: regularity and asymptotics*, SIAM Multiscale Model. Simul. **15** (2017), 1048–1072.

[99] C. Gomez and K. Sølna, *Wave propagation in random waveguide with long-range correlations*, Commun. Math. Sci. **16** (2018), 1557–1596.

[100] A. A. Gonoskov and I. A. Gonoskov, *Suppression of reflection from the grid boundary in solving the time-dependent Schrödinger equation by split-step technique with fast fourier transform*, ArXiv Physics e-prints (2006).
[101] S. A. Goss, R.L. Johnston, and F. Dunn, Comprehensive compilation of empirical ultrasonic properties of mammalian tissues, J. Acoust. Soc. Am. **64** (1978), 423-457.

[102] P. T. Gressman and R. M. Strain, Global classical solutions of the Boltzmann equation with long-range interactions, Proc. Natl. Acad. Sci. **107** (2010), 5744-5749.

[103] ——, Global classical solutions of the Boltzmann equation without angular cut-off, J. Amer. Math. Soc. **24** (2011), 771-847.

[104] L. A. Grzelak, J. Witteveen, M. Suarez-Taboada, and C. W. Oosterlee, The stochastic collocation monte carlo sampler: Highly efficient sampling from "expensive" distributions, Quant. Finance **19** (2019).

[105] Y. Gu and T. Komorovski, Gaussian fluctuations from random schrödinger equation, Commun. Partial. Differ. Equ. **46** (2021), 201-232.

[106] Y. Gu, T. Komorovski, and L. Ryzhik, The Schrödinger equation with spatial white noise: The average wave function, J. Differ. Equ. **274** (2018), 2113-2138.

[107] H. Haeno and F. Michor, The evolution of tumor metastases during clonal expansion, J. Theor. Biol. **263** (2010), 30-44.

[108] L. Hanin, J. Rose, and M. Zaider, A stochastic model for the sizes of detectable metastases, J. Theor. Biol. **243** (2006), 407-417.

[109] A Hanyga, Multidimensional solutions of time-fractional diffusion-wave equations, Proc. R. Soc. Lond. A. **458** (2002), 933-957.

[110] A Hanyga and V. E Rok, Wave propagation in micro-heterogeneous porous media: A model based on an integro-differential wave equation, J. Acoust. Soc. Am. **107** (2000), 2965-2972.

[111] D. Hart, E. Shochat, and Z. Agur, The growth law of primary breast cancer as inferred from mammography screening trials data, Br. J. Cancer **78** (1998), 382-7.

[112] N. Hartung, Efficient resolution of metastatic tumour growth models by reformulation into integral equations, Discret. Contin. Dyn. S. B **20** (2015), 445-467.

[113] N. Hartung, S. Mollard, D. Barbolosi, A. Benabdallah, G. Chapuisat, G. Henry, S. Giacometti, A. Iliadis, J. Ciccolini, C. Faivre, and F. Hubert, Mathematical modeling of tumor growth and metastatic spreading: validation in tumor-bearing mice, Cancer Res. **74** (2014), 6397-6407.

[114] L. G. Henyey and J. Greenstein, Diffuse radiation in the galaxy, Astrophys. J. (1941), 70-83.

[115] T. Ho, L. Landau, and A. Wilkins, On the weak coupling limit for a fermi gas in a random potential, Rev. Math. Phys. **5** (1993), 209-298.

[116] S. Holm, Waves with power-law attenuation, Springer Cham, 2019.

[117] S. Holm and R. Sinkus, A unifying fractional wave equation for compressional and shear wave, J. Acoust. Soc. Am. **127** (2010), 542-548.

[118] H. Hurst, Long-term storage capacity of reservoirs, Trans. Am. Soc. Civ. Eng. **116** (1951), 770-808.

[119] ——, Methods of using long-term storage in reservoirs, P I CIVIL ENG-CIV EN Part I (1955), 519-577.

[120] A. Ishimaru, Wave propagation and scattering in random media, vol. 2, Academic Press, London, 1978.

[121] ——, Wave propagation and scattering in random media and rough surfaces, Proceedings of the IEEE **79** (1991), 1359-1366.
[122] K. Iwata, K. Kawasaki, and N. Shigesada, *A dynamical model for the growth and size distribution of multiple metastatic tumors*, J. Theor. Biol. **203** (2000), 177-186.

[123] S. L. Jacques, *Optical properties of biological tissues: A review*, Phys. Med. Biol. **58** (2013), R37-61.

[124] J. H. Jeans, *Stars, gaseous, radiative transfer of energy*, Mon. Notices Royal Astron. Soc. **78** (1917), 28-36.

[125] S. Jin, P. Markowich, and C. Sparber, *Mathematical and computational methods for semiclassical Schrödinger equations*, Acta Numer. **20** (2011), 121-209.

[126] B. Katsnelson, V. Petnikov, and J. Lynch, *Fundamentals of shallow water acoustics*, Springer, New York, 2012.

[127] O. Katz, P. Heidmann, M. Fink, and S. Gigan, *Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations*, Nature Photon **8** (2014), 784-790.

[128] R. Z. Khasminskii, *A limit theorem for solutions of differential equations with random right hand side*, Theory Probab. Appl. **11** (1966), 390-406.

[129] ——, *On stochastic processes defined by differential equations with a small parameter*, Theory Probab. Appl. **11** (1966), 211-228.

[130] M. Kiss, T. Varghese, and T. Hall, *Viscoelastic characterization of in vitro canine tissue*, Phys. Med. Biol. **49** (2004), 4207-4218.

[131] T. Komorowski and E. Nieznaj, *On the asymptotic behavior of solutions of the heat equation with a random, long-range correlated potential*, Potential Anal. **33** (2009), 175-197.

[132] T. Komorowski, A. Novikov, and L. Ryzhik, *Evolution of particle separation in slowly decorrelating velocity fields*, Commun Math Sci **10** (2012), 767-786.

[133] ——, *Homogenization driven by a fractional brownian motion: the shear layer case*, SIAM Multiscale Model. Simul. **12** (2014), 440-457.

[134] T. Komorowski and L. Ryzhik, *On asymptotics of a tracer advected in a locally self-similar correlated flow*, Asymptot. Anal. **53** (2007), 159-187.

[135] ——, *Passive tracer in a slowly decorrelating random flow with a large mean*, Nonlinearity **20** (2007), 1215-1239.

[136] S. Koscielny, M. Tubiana, M.G. Lê, J. Valleron, H. Mouriesse, G. Contesso, and D. Sarrazin, *Breast cancer: relationship between the size of the primary tumour and the probability of metastatic dissemination*, Br. J. Cancer **49** (1984), 709-715.

[137] W. A. Kuperman and F. Ingenito, *Attenuation of the coherent component of sound propagating in shallow water with rough boundaries*, J. Acoust. Soc. Am. **61** (1977), 1178-1187.

[138] W. A. Kuperman and J. F. Lynch, *Shallow-water acoustics*, Phys. Today **57** (2004), 55-61.

[139] H. J. Kushner, *Approximation and weak convergence methods for random processes, with applications to stochastic systems theory*, MIT Press Series in Signal Processing, Optimization, and Control, 6, MIT Press, Cambridge, MA, 1984.

[140] B. Lapeyre, E. Pardoux, and R. Sentis, *Introduction to monte-carlo methods for transport and diffusion equations*, Oxford University Press, 2003.

[141] N. Lerner, Y. Morimoto, and K. Pravda-Starov, *Hypoelliptic estimates for a linear model of the Boltzmann equation without angular cutoff*, Commun. Part. Diff. Eq. **37** (2012), 234-284.

[142] H. Louvin, E. Dumontel, T. Lelièvre, M. Rousset, and C. M. Diop, *Adaptive multilevel splitting for monte carlo particle transport*, EPJ Nuclear Sci. Technol. **3** (2017).
[143] I. Lux and L. Koblinger, Monte carlo particle transport methods: neutron and photon calculations, CRC Press, 1991.

[144] T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoam. **14** (1998), 215–310.

[145] R. Magnanini and F. Santosa, Wave propagation in a 2-d optical waveguide, SIAM J. Appl. Math **61** (2000), 1237–1252.

[146] B. Mandelbrot, Une classe de processus stochastiques homothétiques à soi; application à loi climatologique de h.e. hurst, Comptes Rendus Acad. Sci. Paris **240**, 3274-3277.

[147] B. Mandelbrot and J. Wallis, Noah, joseph and operational hydrology, Water Resour. Res. **4** (1968), 909–918.

[148] A.A. Maradudin, T. Michel, A. R. McGurn, and E.R. Méndez, Enhanced backscattering of light from a random grating, Ann. Phys. **203** (1990), 255–307.

[149] D. Marcuse, Theory of dielectric optical waveguides, Academic press, New York, 1991.

[150] L. Margerin, A. Bajaras, and M. Campillo, A scalar radiative transfer model including the coupling between surface and body waves, Geophys. J. Int. **219** (2019), 1092–1108.

[151] J. M. Martin and S. M Flatté, Intensity images and statistics from numerical simulation of the wave propagation in 3-d random media, Appl. Optim. **247** (1988), 2111–2126.

[152] R. Marty, Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations, ESAIM Probab. Stat. **9** (2005), 165–184.

[153] R. Marty and K. Sølna, Acoustic waves in long range random media, SIAM J. Appl. Math. **69** (2009), 1065–1083.

[154] __________, A general framework for waves in random media with long-range correlations, Ann. Appl. Probab. **21** (2011), 115–139.

[155] __________, Asymptotic behavior of oscillatory fractional processes, Séminaire de Probabilités XLIV (C. Donati-Martin, A. Lejay, and A. Rouault, eds.), Springer Berlin Heidelberg, Berlin, Heidelberg, 2012, pp. 247–269.

[156] B. Maslowsky and D. Nualart, Evolution equation driven by a fractional brownian motion, J. Funct. Anal. **202** (2003), 277–305.

[157] R. I. McLachlan, G. Quispel, and Reinout W., Splitting methods, Acta Numer. **11** (2002), 341–434.

[158] A. Messaoudi, Radiative transfer models for acoustic waves in a randomly fluctuating medium with boundaries: boundary effects and weak localization, Ph.D. thesis, Aix Marseille University, 2023.

[159] J.S. Michaelson, M. Silverstein, J. Wyatt, G. Weber, R. Moore, E. Halpern, D.B. Kopans, and K. Hughes, Predicting the survival of patients with breast carcinoma using tumor size, Cancer **95** (2002), 713–723.

[160] F. Michor, M.A. Nowak, and Y. Iwasa, Stochastic dynamics of metastasis formation, J. Theor. Biol. **240** (2006), 521–530.

[161] L. Miller, Refraction of high-frequency waves density by sharp interfaces and semiclassical measures at the boundary, J. Math. Pures Appl. **79** (2000), 227–269.

[162] S. P. Näsholm and S. Holm, On a fractional zener elastic wave equation, fcaa **16** (2013), 26–50.

[163] J. Nevard and J.B. Keller, Homogenization of rough boundaries and interfaces, SIAM J. Appl. Math. **57** (1997), 1660–1686.
[164] P. K. Newton, J. Mason, K. Bethel, L. Bazhenova, J. Nieva, L. Norton, and P. Kuhn, *Spreaders and sponges define metastasis in lung cancer: a Markov chain Monte Carlo mathematical model*, Cancer Res. **73** (2013), 2760–2769.

[165] P. K. Newton, J. Mason, K. Bethel, L. A. Bazhenova, J. Nieva, and P. Kuhn, *A stochastic Markov chain model to describe lung cancer growth and metastasis*, PLoS ONE **7** (2012), e34637.

[166] S. Nicolle, M. Lounis, R. Willinger, and J. F. Palierne, *Shear linear behavior of brain tissue over a large frequency range*, Biorheology **42** (2005), 209–223.

[167] U. M. Noebauer and S. A. Sim, *Monte carlo radiative transfer*, Living rev. comput. astrophys. **5** (2019), 1.

[168] D. Nualart and A. Răşcanu, *Differential equations driven by fractional brownian motion*, Collect. Math. **53** (2002), 55–81.

[169] J. A. Ogilvy, *Theory of wave scattering from random rough surfaces*, CRC Press, 1991.

[170] K. Pantel, R. J. Cote, and O. Fodstad, *Detection and Clinical Importance of Micrometastatic Disease*, J. Natl. Cancer Inst. **91** (1999), 1113–1124.

[171] G. C. Papanicolaou and W. Kohler, *Asymptotic theory of mixing stochastic ordinary differential equations*, Comm. Pure Appl. Math **27** (1974), 641–668.

[172] G. C. Papanicolaou and K. Sølna, *Wavelet based estimation of local kolmogorov turbulence*, Long-range dependence: theory and applications (P. Doukhan, G. Oppenmeim, and M. S. Taqqu, eds.), Birkhauser, 2002, pp. 473–507.

[173] G. C. Papanicolaou, D. Stroock, and S. R. S. Varadhan, *Martingale approach to some limit theorem*, Statistical Mechanics, Dynamical Systems and the Duke Turbulence Conference (D. Ruelle, ed.), Duke Univ. Math. Ser., 1977, pp. 1–120.

[174] C. I. Pekeris, *Theory of propagation of explosive sound in shallow water*, Propagation of Sound in the Ocean, Geological Society of America, 1948.

[175] S. Powell, B. T. Cox, and S. R. Arridge, *A pseudospectral method for solution of the radiative transport equation*, J. Comput. Phys. **384** (2019), 376–382.

[176] J. Przybilla and M. Korn, *Monte carlo simulation of radiative energy transfer in continuous elastic random media - three-component envelopes and numerical validation*, Geophys. J. Int. (2008), 566–576.

[177] D Ren, X Shen, C Li, and X Cao, *The fractional kelvin-voigt model for rayleigh surface waves in viscoelastic fgm infinite half space*, Mechanics Research Communications **87** (2018), 53–58.

[178] L. Reynolds and N. McCormick, *Approximate two-parameter phase function for light scattering*, J. Opt. Soc. Am. **70** (1980), 1206–1212.

[179] W. Rudin, *Real and complex analysis*, McGraw-Hill, New York, 1987.

[180] L. Ryzhik, G. C. Papanicolaou, and J. B. Keller, *Transport equations for elastic and other waves in random media*, Wave motion **24** (1996), 327–370.

[181] __________, *Transport equations for waves in a half-space*, Commun. Partial. Differ. Equ. **22** (1997), 1869–1910.

[182] S. G. Samko, A. A. Kilbas, and O. I. Marichev, *Fractional integrals and derivatives*, Gordon and Breach, 1993.

[183] A. Santenac and J. Daillant, *Statistical aspects of wave scattering at rough surface*, X-ray and Neutron Reflectivity, Lecture Notes in Physics (J. Daillant and A. Gibaud, eds.), vol. 770, Springer, Berlin, Heidelberg, 2009, pp. 59–84.
[184] F. Sayas, O. Bruno, and V. Dominguez, *Convergence analysis of a high-order nystrom integral-equation method for surface scattering problems*, Numer. Math. **124** (2013), 603–645.

[185] A. Schuster, *Radiation through a foggy atmosphere*, Astrophys. J. **21**, 1–22.

[186] J.G. Scott, D. Basanta, A.R. Anderson, and P. Gerlee, *A mathematical model of tumour self-seeding reveals secondary metastatic deposits as drivers of primary tumour growth*, J. R. Soc. Interface **10** (2013), 20130011.

[187] F Shi, M.J.S. Lowe, and R.V. Craster, Diffusely scattered and transmitted elastic waves by random rough solid-solid interfaces using an elastodynamic kirchhoff approximation **95** (2017), 214305.

[188] C. Sidi and F. Dalaudier, *Turbulence in the stratified atmosphere: recent theoretical developments and experimental results*, Adv. in Space Res. **10** (1990), 25–36.

[189] I. Simonsen, D. Vandembroucq, and S. Roux, *Wave scattering from self-affine surfaces*, Phys. Rev. E **61** (2000), 5914–5917.

[190] R. Sinkus, K. Siegmann, T. Xydeas, M. Tanter, C. Claussen, and M. Fink, *Mr elastography of breast lesions: Understanding the solid/liquid duality can improve the specificity of contrast-enhanced mr mammography*, Magn. Reson. Med. **58** (2007), 1135–1144.

[191] K. Sølna, *Acoustic pulse spreading in a random fractal*, SIAM J. Appl. Math. **63** (2003), 1764–1788.

[192] J. Spanier and E. M. Gelbard, *Monte carlo principles and neutron transport problems*, Dover Publications, New York, 2008.

[193] H. Spohn, *Derivation of the transport equation for electrons moving through random impurities*, Jour. Stat. Phys. **17** (1977), 385–412.

[194] G. Strang, *On the construction and comparison of difference schemes*, SIAM J. Numer. Anal. **5** (1968), 506–517.

[195] B. E. Stribling, B. M. Welsh, and M. C. Roggemann, *Optical propagation in non-kolmogorov atmospheric turbulence*, Proc. SPIE 2471, Atmospheric Propagation and Remote Sensing IV (1995).

[196] J. W. Strohbehn, *Laser beam propagation in the atmosphere*, Springer, Berlin, 1978.

[197] D. W. Stroock and S. R. S. Varadhan, *Multidimensional diffusion processes*, Springer, Berlin, 1979.

[198] N. V. Sushilov and R. S. C. Cobbold, *Frequency domain wave equation and its time-domain solutions in attenuating media*, J. Acoust. Soc. Am. **115** (2003), 1431–1435.

[199] T. L. Szabo, *Time domain wave equations for lossy media obeying a frequency power law*, J. Acoust. Soc. Am. **96** (1994), 491–500.

[200] D. Talay and L. Tubaro, *Expansion of the global error for numerical schemes solving stochastic differential equations*, Stoch. Anal. Appl. **8** (1991), 94–120.

[201] F. D. Tappert, *The parabolic approximation method in wave propagation and underwater acoustics*, Lecture Notes in Phys., Spinger, Berlin **70** (1977), 224–287.

[202] M. S. Taqqu, *Weak convergence to fractional brownian motion and to the rosenblatt process*, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete **31** (1975), 287–302.

[203] __________, *Law of the iterated logarithm for sums of non-linear functions of gaussian variables that exhibit a long range dependence*, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete **40** (1977), 203–238.
[204] M. J. van de Vijver, Y. D. He, L. J. van't Veer, H. Dai, A. A. M. Hart, D. W. Voskuil, G. J. Schreiber, J. L. Peterse, C. Roberts, M. J. Marton, M. Parrish, D. Atsma, A. Witteveen, A. Glas, L. Delahaye, T. van der Velde, H. Bartelink, S. Rodenhuis, E. T. Rutgers, S. H. Friend, and R. Bernards, *A gene-expression signature as a predictor of survival in breast cancer*, N. Engl. J. Med. **347** (2002), 1999–2009.

[205] M. van den Berg and J.T. Lewis, *Brownian motion on hypersurface*, Bull. London Math. Soc. **17** (1985), 144–150.

[206] C. Villani, *A review of mathematical topics in collisional kinetic theory*, Handbook of mathematical fluid dynamics, Vol. I, North-Holland, Amsterdam, 2002, pp. 71–305.

[207] R. Viskanta and M. P. Mengüç, *Radiation heat transfer in combustion systems*, Prog. Energy Combust. Sci. **13** (1987), 97–160.

[208] R. Weron, *On the chambers-mallows-stuck method for simulating skewed stable random variables*, Stat. Probab. Lett. **28** (1996), 165 – 171.

[209] WHO, *Cancer fact sheet*, 2015, http://www.who.int/mediacentre/factsheets/fs297/en/ (accessed 14 Jan 2016).

[210] M. Wismer and R. Ludwig, *An explicit numerical time domain formulation to simulate pulsed pressure waves in viscous fluids exhibiting arbitrary frequency power law attenuation*, IEEE Trans. Ultrason. Ferro- electr. Freq. Control **42** (1995), 1040–1049.

[211] M. Zähle, *Integration with respect to fractal functions and stochastic calculus. i*, Probab. Theory Relat. Fields **111** (1998), 333–374.

[212] A. Zilberman, E. Golbraikh, N. S. Kopeika, A. Virtser, I. Kupershmidt, and Y. Shtemler, *Lidar study of aerosol turbulence characteristics in the troposphere: Kolmogorov and non-kolmogorov turbulence*, Atmos. Res. (2008), 66–77.