Some suggested projects for STT 962 (links are hot).  You will present to the class using the blackboard, or computer if you prefer. 

Project idea #1:  Read a paper and present it to the class.  You need not understand every detail, just tell us the main ideas, and maybe show an interesting computation or proof from the paper.  Here are some suggested papers (links are hot).

M.M. Meerschaert and P. Straka, Inverse stable subordinators, Mathematical Modeling of Natural Phenomena, Vol. 8 (2013), No. 2, pp. 1–16. Click here to download R codes used in this paper. See also Remark 2.12 in our textbook.

M.M. Meerschaert, E. Nane and Y. Xiao, Fractal dimensions for continuous time random walk limits, Statistics and Probability Letters, Vol. 83 (2013), No. 4, pp. 1083–1093.

M.M. Meerschaert, P. Straka, Y. Zhou, and R.J. McGough, Stochastic solution to a time-fractional attenuated wave equation, Nonlinear Dynamics, Vol. 70 (2012), No. 2, pp. 1273–1281.

A. Kumar, M.M. Meerschaert, and P. Vellaisamy, Fractional Normal Inverse Gaussian Diffusion, Statistics and Probability Letters, Vol. 81 (2011) pp. 146–152.

M.M. Meerschaert, E. Nane, and P. Vellaisamy, The fractional Poisson process and the inverse stable subordinator, Electronic Journal of Probability, Vol. 16 (2011), Paper no. 59, pp. 1600–1620.

A. Chakrabarty and M. M. Meerschaert, Tempered stable laws as random walk limits, Statistics and Probability Letters, Vol. 81 (2011), No. 8, pp. 989-997.

S. Cohen, M. M. Meerschaert and J. Rosiński, Modeling and simulation with operator scaling, Stochastic Processes and Their Applications, Vol.120 (2010) pp. 2390–2411. Click here for an extended version with additional examples and details. Click here to download MAPLE software used to compute the model parameters, and here for MATLAB software to implement the sample path simulations.

K. M. Hill, L. DellAngelo, and M. M. Meerschaert, Heavy tailed travel distance in gravel bed transport: An exploratory enquiry, Journal of Geophysical Research, Vol. 115 (2010), p. F00A14, doi:10.1029/2009JF001276.  See especially Appendix A.

B. Baeumer, M. M. Meerschaert and M. Naber, Stochastic models for relativistic diffusion, Physical Review E, Vol. 82 (2010), pp. 011132.

M.M. Meerschaert, E. Nane, P. Vellaisamy, Fractional Cauchy problems on bounded domains, The Annals of Probability, Vol. 37 (2009), No. 3, pp. 979–1007. Click here to read the accompanying "Members' Discovery" article from the July 2009 IMS Bulletin.

B. Baeumer, M.M. Meerschaert and E. Nane, Space-time duality for fractional diffusion, Journal of Applied Probability, Vol. 46 (2009), pp. 1100-1115.

M.M. Meerschaert, E. Nane, Y. Xiao, Correlated continuous time random walks, Statistics and Probability Letters, Vol. 79 (2009), pp. 1194-1202.

B. Baeumer, M.M. Meerschaert, E. Nane, Brownian subordinators and fractional Cauchy problems, Transactions of the American Mathematical Society, Vol. 361 (2009), No. 7, pp. 3915–3930.

M.M. Meerschaert, S. Stoev, Extremal limit theorems for observations separated by random power law waiting times, Journal of Statistical Planning and Inference, Vol.139 (2009), pp. 2175-2188.

M.M. Meerschaert, S.W. Wheatcraft, Fractional Conservation of Mass, Advances in Water Resources, Vol. 31 (2008), pp. 1377–1381.

B. Baeumer, M. Kovács, M.M. Meerschaert, Fractional reproduction-dispersal equations and heavy tail dispersal kernels, Bulletin of Mathematical Biology, Vol. 69 (2007), pp. 2281-2297.

T.J. Kozubowski, M.M. Meerschaert, K. Podgórski, Fractional Laplace Motion, Advances in Applied Probability, Vol. 38 (2006), No. 2, pp. 451-464.

M.M. Meerschaert, H.P. Scheffler, Stochastic model for ultraslow diffusion, Stochastic Processes and Their Applications, Vol. 116 (2006), No. 9, pp. 1215-1235.

B. Baeumer, M.M. Meerschaert, and S. Kurita, Inhomogeneous fractional diffusion equations, Fractional Calculus and Applied Analysis, Vol. 8, No 4 (2005), pp. 371-386.

M.M. Meerschaert and C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations Journal of Computational and Applied Mathematics, Vol. 172 (2004), No. 1, pp. 65-77.

Project idea #2:  Carefully go step by step through the derivation of the characteristic function for a stable law in Section 3.2, including the dominated convergence arguments.

Project idea #3:  Carefully go through the regular variation arguments  in the "details" in Section 4.1.  Explain why nP(a_nW>x) converging to some G(x) implies that a_n is regularly varying and V(x)=P(W>x) is regularly varying and G(x) is a power law.

Project idea #4:  Write an R simulation to compute and plot solutions to the space and time fractional diffusion equation.  Present to the class and discuss features of the solution curves.  What are their scaling properties?  What is their tail behavior?