OSU ACTUARIAL SCIENCE: 1984 to NOW This is an extended overview of an article published in abbreviated form in the OSU Department of Mathematics Alumni Newsletter, Fall, 2017.

E. Waymire (2017): OSU ACTUARIAL SCIENCE: 1984 to NOW

Current Research Interests

Research Interests

Applications of probability and stochastic processes to problems involving flow and/or dispersion. Mathematically this involves the interplay between probability and pdes as a two-way avenue. Example areas of application include fluid flows, especially the incompressible Navier-Stokes equations, and dispersion of solutes in heterogeneous porous media.

Selected Publications and Preprints

Chen, L.,R.B, Guenther, S-C. Kim, E.A. Thomann, E.C. Waymire (2008): A Rate of Convergence for the LANS alpha Regularization of Navier-Stokes Equations Journal of Mathematical Analysis and Applications, vol. 348, pp. 637--649.

Waymire, E., S. Williams (2010): T-martingales, size-biasing and tree polymer cascades, eds Barral, J., S. Seuret, Recent Developments in Fractals and Related Fields, 353-382, Birkhauser Boston, (post pub. corrected file, 10/30/2011)).

Appuhamillage, T., V. Bokil, E. Thomann, E. Waymire, B. Wood (2011): Occupation and local times for skew Brownian motion with applications to dispersion across an interface, Annals of Applied Probability. vol. 21(1), pp. 183--214. (Correction: Annals of Applied Probability. vol. 21, No. 5, (2011), pp. 2050--2051, 2nd Errata To Appear)

Johnson, T, Waymire, E. (2011): Tree polymers in the infinite volume limit at critical strong disorder, J. Appld. Probab., vol. 48(3), pp. 885--891.

Ramirez, J., E. Thomann, E. Waymire (2013): Advection-Disperson Across Interfacesn Statistical Science, Vol 28(4), 487-509.

Dey, P., E. Waymire (2015): On Normalized Multiplicative Cascades Under Strong Disorder Elect. Comm. Prob. vol. 20,, pp. 1-13.

Dascaliuc, R. N. Michalowski, E. Thomann, E. Waymire (2015): Symmetry Breaking and Uniqueness for the Incompressible Navier-Stokes Equations Chaos: Journal of Am. Inst. Phys.

Ramirez, J., E. Thomann, E. Waymire (2015): Continuity of Local Time: An applied perspective The Fascination of Probability, Statistics and their Applications: Festschrift in Honour of Ole E. Barndorff-Nielsen , eds., Mark Podolskij, Robert Steizer, Steen Thorbjørnsen, Almut Veraart

Dascaliuc, R., N. Michalowski, E. Thomann, E. Waymire (2017): A Delayed Yule Process Proc. Amer. Math Soc.

Jennings-Shafer, C., D. Skinner, E. Waymire (2018): When Fourth Moments Are Enough Rocky Mountain Journal of Mathematics

Peckham, S., E. Waymire, P. De LeenHeer (2018): Critical Thresholds for Eventual Extinction in Randomly Disturbed Population Growth Models Journal of Mathematical Biology

Dascaliuc, R., E. Thomann, E. Waymire (2018): Stochastic Explosion and Non-Uniqueness for α-Riccati Equation Journal of Math.Anal. and Appl., vol 476(1), 53-85.

Bokil, V., N. Gibson,L.S.Nguyen, E. Thomann, E. Waymire (2019): An Euler-Maruyama Method for Diffusion Equations with Discontinuous Coefficients and a Family of Interface Conditions, Journal of Computational and Applied Mathematics.

Dascaliuc, R., N. Michalowski, E. Thomann, E. Waymire (2019): Complex Burgers Equation: A probabilistic perspective Sojourns in Probability and Statistical Physics", Vol 1, ed Vladas Sidoravicius, Springer NY

Dascaliuc, R., T. Pham, , E. Thomann, E. Waymire (2022): Doubly Stochastic Yule Cascades (Part I): The explosion problem in the time--reversible case, Journal of Functional Analysis vol. 284(1)

Dascaliuc, R., T. Pham, , E. Thomann, E. Waymire (2022): Doubly Stochastic Yule Cascades (Part II): The explosion problem in the non--reversible case Annales Instiut Henri Poincare vol 59(4) pp. 1907-1933

Dascaliuc, R., E., Pham, T., Thomann, E. Waymire (2023): Errata to Stochastic Explosion and Non-Uniqueness for α-Riccati Equation Journal of Math.Anal. and Appl. vol 527, No2

Dascaliuc, R., T. Pham, , E. Thomann, E. Waymire (2024): Transformation of Stochastic Recursions and Critical Phenomena in the Analysis of a Class of Mean Flow Equations (to be submitted) arXiv: 2411.00629v1 Transformation of Stochastic

Recent Books

Bhattacharya, R., E. Waymire (2007): A Basic Course in Probability Theory, Universitext, Springer, NY. (2016) 2nd Edition 2ND EDITION ERRATA

Bhattacharya, R., E. Waymire (2009): Stochastic Processes with Applications, SIAM Classics in Applied Mathematics Series.

Bhattacharya, R., E. Waymire (2021): Random Walk, Brownian Motion, and Martingales, 292 Springer Graduate Text in Mathematics.

Bhattacharya, R., E. Waymire (2022): Stationary Processes and Discrete Parameter Markov Processes , 293 Springer Graduate Text in Mathematics.

Bhattacharya, R., E. Waymire (2023): Continuous Parameter Markov Processes and Stochastic Differential Equations, 299 Springer Graduate Text in Mathematics.

Service

Past Chief Editor, Annals of Applied Probability, 2006—2010
Past Editor, Bernoulli, 1994—2006
Associate Editor, Proceedings of the American Mathematical Society, 2004—2008
Associate Editor, Stochastics and Dynamics, 2013—2018
Associate Editor, Probability Surveys, 2003—present
Past-President, Bernoulli Society for Mathematical Statistics and Probability, 2013—2015.

Education

PhD University of Arizona, 1976

Research areas