David P. Herzog
Dept. of Mathematics
Iowa State University
Office: Carver 474
Email: dherzog "at" iastate "dot" edu
Iowa State Math Department Webpage
Teaching (Fall '18)
Note: All course materials can be found on Canvas.
My main interests are in stochastic analysis, in particular stochastic differential equations. I also have interests in applied mathematics, and some of my research in this area has been featured in popular press: DukeToday, Pharmacy Times, Futurity, WUNC, Healio, ACSH, ICT, AHC Media. Currently, my research is supported in part by grant DMS-1612898 from the National Science Foundation.
Exponential relaxation of the Nosé-Hoover thermostat under Brownian heating (PDF)
(D.P. Herzog). To appear in Commun. Math. Sci..
The generalized Langevin equation with a power-law memory in a nonlinear potential well (PDF)
(N.E. Glatt-Holtz, D.P. Herzog, S.A. McKinley, and H.D. Nguyen). Submitted.
Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials (PDF)
(D.P. Herzog and J.C. Mattingly). Submitted.
Scaling and saturation in infinite-dimensional control problems with applications to SPDEs (PDF)
(N.E. Glatt-Holtz, D.P. Herzog and J.C. Mattingly). Annals of PDE 4 no. 2 , 103 pages (2018).
Geometric ergodicity of two-dimensional Hamiltonian systems with a Lennard-Jones-Like repulsive potential (PDF)
(B. Cooke, D.P. Herzog, J.C. Mattingly, S.A. McKinley, S.C. Schmidler). Commun. Math. Sci. 15 no. 7 pp. 1987-2025 (2017).
The small-mass limit for Langevin dynamics with unbounded coefficients and positive friction (PDF)
(D.P. Herzog, S. Hottovy and G. Volpe). J. Stat. Phys. 163 no. 3 pp.659-673 (2016).
Noise-induced stabilization of planar flows II (PDF)
(D.P. Herzog and J.C. Mattingly). Electron. J. Probab. 20 no. 113 pp.1-37 (2015).
Noise-induced stabilization of planar flows I (PDF)
(D.P. Herzog and J.C. Mattingly). Electron. J. Probab. 20 no. 111 pp.1-43 (2015).
A practical criterion for positivity of transition densities (PDF)
(D.P. Herzog and J.C. Mattingly). Nonlinearity 28 pp.2823-2845 (2015).
Impact of coverage-dependent marginal costs on optimal HPV vaccination strategies (PDF)
(M.D. Ryser, K. McGoff, D.P. Herzog, D.J. Sivakoff and E.R. Myers). Epidemics 11 pp.32-47 (2015).
An extension of Hormander's hypoellipticity theorem (Journal)
(D.P. Herzog and N. Totz). Potential Anal. 42 pp.403-433 (2015).
The transition from ergodic to explosive behavior in a family of stochastic differential equations (PDF)
(J. Birrell, D.P. Herzog and J. Wehr). Stochastic Process. Appl. 122 pp.1519-1539 (2012).
Ergodic properties of a model for turbulent dispersion of inertial particles
(K. Gawedzki, D.P. Herzog and J. Wehr). Comm. Math. Phys. 308 pp.49-80 (2011).
Geometry's fundamental role in the stability of stochastic differential equations (PDF)
Ph.D. Dissertation (2011).