Courses (Spring 2025)

• MAP 4113 Probability
• MAA 6238 Measure and Probability
• MAS 3105 Matrix and Linear Algebra

Measure and Probability Lecture Notes

These notes are for a two-semester sequence in measure-theoretic probability theory: pdf file (last updated November 5, 2024)

Software

idp

Description: A Python package for working with the iterated Dirichlet process (see [Donald and Swanson, 2025]).
Documentation: https://jason-swanson.github.io/idp
Source Code: https://github.com/jason-swanson/idp

Research Monograph

Swanson, J. (2024) The Principles of Probability: From Formal Logic to Measure Theory to the Principle of Indifference (240 pages). To appear in Lecture Notes in Mathematics, Springer. arxiv:2504.21522

Papers

• Donald, E., & Swanson, J. (2025). The iterated Dirichlet process and applications to Bayesian inference (51 pages, 5 figures, 8 tables). Preprint. arxiv:2505.00451
• Donald, E., & Swanson, J. (2025). An Aldous-Hoover type representation for row exchangeable arrays (14 pages). Preprint. arxiv:2504.21584
• Kurtz, T. G., & Swanson, J. (2022a). Finite Markov chains coupled to general Markov processes and an application to metastability I. In Stochastic analysis, filtering, and stochastic optimization (pp. 293–307). Springer, Cham. https://doi.org/10.1007/978-3-030-98519-6_12, arXiv:1906.03212
• Kurtz, T. G., & Swanson, J. (2022b). Finite Markov chains coupled to general Markov processes and an application to metastability II. In Stochastic analysis, filtering, and stochastic optimization (pp. 309–337). Springer, Cham. https://doi.org/10.1007/978-3-030-98519-6_13, arXiv:2101.07290
• Burdzy, K., Nualart, D., & Swanson, J. (2013). Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion. Probability Theory and Related Fields, 1–36. https://doi.org/10.1007/s00440-013-0511-2, arXiv:1210.1560
• Nualart, D., & Swanson, J. (2013). Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion II. Electron. Commun. Probab., 18, nos. 81, 1–11. https://doi.org/10.1214/ECP.v18-2840, arXiv:1303.0892
• Swanson, J. (2013). The Calculus of Differentials for the Weak Stratonovich Integral. In F. Viens, J. Feng, Y. Hu, & E. Nualart (Eds.), Malliavin Calculus and Stochastic Analysis (Vol. 34, pp. 95–111). Springer US. https://doi.org/10.1007/978-1-4614-5906-4_5, arXiv:1103.0341
• Swanson, J. (2011). Fluctuations of the empirical quantiles of independent Brownian motions. Stochastic Process. Appl., 121(3), 479–514. https://doi.org/10.1016/j.spa.2010.11.012, arXiv:0812.4102
• Burdzy, K., Pal, S., & Swanson, J. (2010). Crowding of Brownian spheres. ALEA Lat. Am. J. Probab. Math. Stat., 7, 193–205. https://alea.impa.br/articles/v7/07-10.pdf, arXiv:1002.1057
• Burdzy, K., & Swanson, J. (2010). A change of variable formula with Itô correction term. Ann. Probab., 38(5), 1817–1869. https://doi.org/10.1214/09-AOP523, arXiv:0802.3356
• Nourdin, I., Réveillac, A., & Swanson, J. (2010). The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6. Electron. J. Probab., 15, nos. 70, 2117–2162. https://doi.org/10.1214/EJP.v15-843, arXiv:1006.4238
• Swanson, J. (2007a). Variations of the solution to a stochastic heat equation. Ann. Probab., 35(6), 2122–2159. https://doi.org/10.1214/009117907000000196, arXiv:math/0601007
• Swanson, J. (2007b). Weak convergence of the scaled median of independent Brownian motions. Probab. Theory Related Fields, 138(1–2), 269–304. https://doi.org/10.1007/s00440-006-0024-3, arXiv:math/0507524
• Ott, T. J., & Swanson, J. (2007). Asymptotic behavior of a generalized TCP congestion avoidance algorithm. J. Appl. Probab., 44(3), 618–635. https://doi.org/10.1239/jap/1189717533, arXiv:math/0608476
• Ott, T. J., & Swanson, J. (2006). Stationarity of some processes in transport protocols. SIGMETRICS Perform. Eval. Rev., 34(3), 30–32. https://doi.org/10.1145/1215956.1215969, pdf file
• Swanson, J. (2004). Variations of stochastic processes: Alternative approaches (p. 121). ProQuest LLC, Ann Arbor, MI. ProQuest link, pdf file