Homepage of Philip A. Ernst

Philip A. Ernst, Ph.D.


Associate Professor
(with tenure)
Department of Statistics
Rice University


I am currently an Associate Professor of Statistics (with tenure) at Rice University's Department of Statistics.

My research interests include applied probability, exact distribution theory, mathematical finance, mathematical statistics, operations research, optimal stopping, queueing systems, statistical inference for stochastic processes, and stochastic control.

I am currently a Guest Editor for "In Memoriam: Larry Shepp," a special issue of Stochastic Processes and their Applications. I serve as an Associate Editor of Mathematics of Operations Research, as an Associate Editor of Statistics & Probability Letters, and as an Associate Editor of Stochastics. I also serve as an Editor of Journal of Stochastic Analysis.

To get a taste of some of my current research interests, please see this video of a talk given at the Institute for Mathematics and its Applications. A list of all invited talks may be found here.

I gratefully acknowledge support from the U.S. Army Research Office Young Investigator Program (ARO-YIP-71636-MA), the U.S. Office of Naval Research (N00014-21-1-2672 and N00014-18-1-2192), and the National Science Foundation (DMS-1811936).

Employment

(Jan 2019-present) Associate Professor of Statistics (with tenure)
(July 2018-Dec 2018) Assistant Professor of Statistics and Dobelman Family Junior Chair of Statistics
(July 2014-June 2018) Assistant Professor of Statistics

Education

Ph.D. in Statistics, The Wharton School of the University of Pennsylvania (2014)
M.A. in Statistics, The Wharton School of the University of Pennsylvania (2010)
B.A. cum laude in Statistics, Harvard University (2007)

Research In The News

A 90 Year Old Problem Solved

News


National and International Research Honors

University Research Honors

  • 2019: Awarded Early Tenure at Rice (Two Years Early) Press Release
  • 2019 Rice University School of Engineering Teaching and Research Excellence Award Press Release
  • (July 2018-Dec 2018) Dobelman Family Junior Chair of Statistics Press Release

University Teaching Honors

  • 2021 Rice University George R. Brown Award for Superior Teaching Press Release Rice News
  • 2017 Rice University Nicolas Salgo Outstanding Teaching Award Press Release Rice News
  • 2016 Rice University Sophia Meyer Farb Prize for Teaching (Phi Beta Kappa Teaching Award) Press Release
  • 2015 Rice University Graduate Student Association Faculty Teaching and Mentoring Award Link
  • 2014 University of Pennsylvania Department of Statistics Donald S. Murray Prize for Excellence in Teaching
  • 2009 University of Pennsylvania Prize for Excellence in Teaching by Graduate Students Link

Federal Research Funding

Federal Conference Funding

Local and Private Conference Funding for A symposium on optimal stopping

Selected Works

Legend: (*) denotes a postdoctoral fellow co-author. (**) denotes a Ph.D. student co-author.

  • Ernst, P.A. and Franceschi, S. (2021+) Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary. The Annals of Applied Probability, to appear. PDF Link to Journal
  • Ernst, P.A., Peskir, G., and Zhou, Q.* (2020) Optimal real-time detection of a drifting Brownian coordinate. The Annals of Applied Probability 30(3): 1032-1065. PDF Link to Journal
  • Ernst, P.A., Rogers, L.C.G., and Zhou, Q.* (2020) When is it best to follow the leader? Stochastic Processes and their Applications 130(6): 3394-3407. PDF Link to Journal
  • Ernst, P.A., Shepp, L.A., and Wyner, A.J. (2017) Yule's "nonsense correlation" solved! The Annals of Statistics 45(4): 1789-1809. PDF Link to Journal
  • Ernst, P.A., Rogers, L.C.G, and Zhou, Q.* (2017) The value of foresight. Stochastic Processes and their Applications, 127(12): 3913-3927. PDF Link to Journal Video Talk

Papers Under Preparation

  1. Ernst, P.A., Huang, D.** and Viens, F.G. (2021) Yule’s “nonsense correlation” for Gaussian random walks. PDF
  2. Gerber, S., Markowitz, H.M., Ernst, P.A., Miao, Y.**, Javid, B., and Sargen, P. (2021) The Gerber statistic: a robust co-movement measure for portfolio optimization. PDF

Papers Under Review

  1. Bednarz, E., Ernst, P.A., and Osekowski, A. (2021) On the diameter of the stopped spider process. PDF
  2. Ernst, P.A., Rogers, L.C.G., and Zhou, Q.* (2020) The distribution of Yule's "nonsense correlation." PDF

Papers Under Invited Revision

  1. Ernst, P.A., Kagan, A.M., and Rogers, L.C.G. (2021) The least favorable noise. PDF
  2. Ernst, P.A. and Peskir, G. (2020) Quickest real-time detection of a Brownian coordinate drift. PDF
  3. Ernst, P.A., Brown, L.D., and Shepp, L.A. (2019) Multiple collection estimation of population size: A generalization of "capture-recapture." PDF

Published Papers and Papers in Press

  1. Ernst, P.A., Franceschi, S., and Huang, D.** (2021+) Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant. Stochastic Processes and their Applications, to appear. PDF Link to Journal
  2. Ernst, P.A. and Franceschi, S. (2021+) Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary. The Annals of Applied Probability, to appear. PDF Link to Journal
  3. Ernst, P.A., Imerman, M.B., Shepp, L.A., and Zhou, Q.* (2021+) A martingale approach to the question of fiscal stimulus. Stochastic Processes and their Applications, to appear. PDF Link to Journal
  4. Bruss, F.T., Ernst, P.A., and Huang, D.** (2021+) The rencontre problem. Stochastic Processes and their Applications, to appear. PDF Link to Journal
  5. Ernst, P.A. and Rogers, L.C.G. (2020) The value of insight. Mathematics of Operations Research, 45(4): 1193-1209. PDF Link to Journal
  6. Ernst, P.A., Peskir, G., and Zhou, Q.* (2020) Optimal real-time detection of a drifting Brownian coordinate. The Annals of Applied Probability 30(3): 1032-1065. PDF Link to Journal
  7. Ernst, P.A., Rogers, L.C.G., and Zhou, Q.* (2020) When is it best to follow the leader? Stochastic Processes and their Applications, 130(6): 3394-3407. PDF Link to Journal
  8. Ernst, P.A. and Shaman, P. (2019) The bias mapping of the Yule-Walker estimator is a contraction. Statistica Sinica, 29(4):1831-1849. Link to Journal
  9. Ernst, P.A. and Viens, F.G. (2019) In memory of Larry Shepp: An editorial. High Frequency, 2(2): 74-75. Link to Journal
  10. Ernst, P.A., Kendall, W.S., Roberts, G.O, and Rosenthal, J.S. (2019) MEXIT: Maximal un-coupling times for stochastic processes. Stochastic Processes and their Applications, 129(2): 355-380. PDF Link to Journal
  11. Ernst, P.A. and Soleymani, F. (2019) A Legendre-based computational method for solving a class of Ito stochastic delay differential equations. Numerical Algorithms, 80(4): 1267-1282. PDF Link to Journal
  12. Ernst, P.A., Kimmel, M., Kurpas, M., and Zhou, Q.* (2018) Heavy-tailed distributions in branching process models of secondary cancerous tumors. Advances in Applied Probability, 50(A): 99-114. PDF Link to Journal
  13. Ernst, P.A., Asmussen, S., and Hasenbein, J.J. (2018) Stability and busy periods in a multiclass queue with state-dependent arrival rates. Queueing Systems, 90: 207-224. PDF Link to Journal
  14. Zhou, Q.*, Ernst, P.A., Morgan, K.L, Rubin, D.B., and Zhang, A. (2018) Sequential rerandomization. Biometrika, 105(3): 745-752. PDF Link to Journal
  15. Ernst, P.A., Rogers, L.C.G, and Zhou, Q.* (2017) The value of foresight. Stochastic Processes and their Applications, 127(12): 3913-3927. PDF Link to Journal
  16. Ernst, P.A., Shepp, L.A., and Wyner, A.J. (2017) Yule's "nonsense correlation" solved! The Annals of Statistics 45(4): 1789-1809. PDF Link to Journal
  17. Ernst, P.A. (2017) Minimizing Fisher information with absolute moment constraints. Statistics and Probability Letters 129: 167-170. Link to Journal
  18. Ernst, P.A. and Grigorescu, I. (2017) Asymptotics for the time of ruin in the war of attrition. Advances in Applied Probability 49(2): 388-410. PDF Link to Journal
  19. Ernst, P.A., Thompson, J.R., and Miao, Y.** (2017). Portfolio selection: the power of equal weight. In Models and Reality: A Festschrift for James R. Thompson , pp. 225-236. PDF
  20. Ernst, P.A., Thompson, J.R., and Miao, Y.** (2017) Tukey's transformational ladder for portfolio management. Financial Markets and Portfolio Management 31(3): 317-355. PDF Link to Journal
  21. Ernst, P.A. and Shepp, L.A. (2017) On occupation times of the first and third quadrants for planar Brownian motion. Journal of Applied Probability 54(1): 337-342. PDF Link to Journal
  22. Ernst, P.A., Brown, L.D., Shepp, L.A., and Wolpert, R.L. (2017) Stationary Gaussian Markov processes as limits of stationary autoregressive time series. Journal of Multivariate Analysis 155: 180-186. Link to Journal
  23. Ernst, P.A. (2017) On the arbitrage price of European call options. Stochastic Models 33(1): 48-58. Link to Journal
  24. Ernst, P.A. and Shepp, L.A. (2016) Eliminating a loophole in the national flood insurance program. Law, Probability and Risk 15(4): 251-258. Link to Journal
  25. Ernst, P.A., Pemantle, R., Satopaa, V., and Ungar, L. (2016) Bayesian aggregation of two forecasts in the partial information framework. Statistics and Probability Letters 119: 170-180.
  26. Ernst, P.A. (2016) Exercising control when confronted by the (Brownian) spider. Operations Research Letters 44: 487-490. PDF Link to Journal
  27. Ernst, P.A. and Shepp, L.A. (2016) On the time for Brownian motion to visit every point on a circle. Journal of Statistical Planning and Inference 171: 130-134. PDF Link to Journal
  28. Ernst, P.A. and Shepp, L.A. (2015) Revisiting a theorem of L.A. Shepp on optimal stopping. Communications on Stochastic Analysis 9(3): 419-423. PDF Link to Journal
  29. Ernst, P.A., Foster, D.P., and Shepp, L.A. (2014). On optimal retirement. Journal of Applied Probability 51(2): 333-345. Link to Journal
  30. Ernst, P.A. (2014). Multiple Collection Estimation of Population Size: A Generalization of "Capture-Recapture." Ph.D. thesis.


Current Postdoctoral Fellows (sole advisor)

Former Postdoctoral Fellows (sole advisor)

  • Quan Zhou, Ph.D. (April 2017-August 2019)
    Current Employment: Tenure-track Assistant Professor of Statistics, Texas A&M University

Current Ph.D. students (sole advisor)

Former Ph.D. Students (sole advisor)

Public Outreach

Philip Ernst served as the director of instruction for the July 28-August 2, 2019 summer session of the Tapia Center Say STEM Camp at The Tapia Center for Excellence & Equity at Rice University

In the Media

  • October 20, 2016: Making sense of the 'nonsense correlation' in Rice Engineering Magazine (Fall 2016), p.24 Link
  • May 13, 2016: Rice University Phi Beta Kappa address Press Release

Course Reviews

As an Assistant Professor (tenure-track) and Associate Professor (with tenure) at Rice University, I have taught STAT 310 (undergraduate probability and statistics), STAT 581 (A Ph.D. course in measure-theoretic probability), and STAT 650 (A Ph.D. course in stochastic differential equations). Course reviews may be found below.

As a Ph.D. candidate at Wharton Statistics, I taught STAT 101 (undergraduate business statistics). The course review is below.

STAT 101 Instructor Review