David P. Herzog
Dept. of Mathematics
Iowa State University
Office: Carver 474
Email: dherzog "at" iastate "dot" edu
Iowa State Math Department Webpage
Teaching (Spring 2020)
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 grants DMS-1612898 and DMS-1855504 from the National Science Foundation.
Gamma calculus beyond Villani and explicit convergence estimates for Langevin dynamics with singular potentials (PDF)
(F. Baudoin, M. Gordina, and D.P. Herzog). Submitted
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). To appear in Nonlinearity.
Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials (PDF)
(D.P. Herzog and J.C. Mattingly). Comm. Pure Appl. Math. 72 no. 10 pp. 2231-2255 (2019)
Exponential relaxation of the Nosé-Hoover thermostat under Brownian heating (PDF)
(D.P. Herzog). Commun. Math. Sci. 16 no. 8 pp. 2231-2260 (2018)
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).