Lecture Notes

"Macroscopic Dimension" (Ithaca; June 2015; Adventures in Self-Similarity)

"Dissipation and High Disorder" (Princeton; March 2015; Columbia-Princeton Probab. Day)

"Nonlinear Noise Excitation" (Evanston; October 2014; Midwest Probab. Colloq., Lecture I)

"Intermittency and Multifractality" (Evanston; October 2014; Midwest Probab. Colloq., Lecture II)

"On the Chaotic Character of Some Parabolic SPDEs" (Banff; September 2011; BIRS)

"An Asymptotic Theory for Randomly-Forced Heat Equations" (Guanajuato; March 2009; CIMAT)

"Brownian motion and Thermal capacity" (Greifswald September 2008)

"SPDEs without PDEs" (Madison May 2008)

"Lévy processes and stochastic partial differential equations" (Copenhagen Aug 2007) 

"Dynamical processes" (Colorado May 2007) 

"On some applications of stable processes" (Houston May 2007) 

"Slices of the Brownian sheet" (Seattle August 2006); David Levin's movie (avi) (67.3 MB)

"Two tutorials on additive Lévy processes" (Seattle August 2006)

"Two lectures on additive Lévy processes" (WPA May 06; Taipei)

"Exceptional Times and Invariance for Dynamical Random Walks"

"Estimates for the laws of functionals of a Brownian sheet: recent progress and open problem," Swiss Probability Seminar

"An Introduction to Parabolic SPDEs"; (Lectures in Probability & Stochastic Processes XI; ISI-Delhi Center; Nov 2016)

"Gaussian Analysis" (Math. 7880; Spring 2015)

"Linear Models" (Math 6010; Fall 2011)

"Lévy Processes (Math 7880, Spring 2011)

"Introductory Lectures on Stochastic Calculus" (Math 7880, Spring 2008)

"Summer School on Lévy Processes and Their Applications" (5 lectures at the Sandeberg Manor, Aug '07):

• • • • Lecture 1: Measure and Dimension

      • Lecture 2: The Range of a Lévy Process

      • Lecture 3: Harmonic Analysis

      • Lecture 4: More on the Range

      • Lecture 5 [Terminus]: Capacity

      • Handout on Riesz kernels

"Tutorial on SPDEs" (Utah VIGRE Minicourse May '06)

Slightly idiosyncratic, but hopefully fun, notes on Discrete Math (Summer 2015)

"Lecture notes on mathematical statistics" (Math 6070):

• • • • Introduction to Probability.

      • Introduction to Statistics.

      • Chi-Squared Tests.

      • Empirical Processes, and the Kolmogorov-Smirnov Statistic.

      • Density Estimation.

"Lecture notes on the ergodic theorem" (Math 7880)

"Lecture notes on Donsker's invariance principle" (Math 7880)

"Lecture notes on linear statistical models" (Math 6010):

• • • • Assessing Normality,

      • Least Squares and Projections,

      • Simple Linear Regression.

"Mathematical Probability," (Math 6040), The University of Utah.

REU Notes on "Random Walks," The University of Utah.

"Lectures on Multiparameter Processes," EPF-Lausanne.

"Lectures on the Brownian sheet," U. Wisconsin-Madison.