Andrew Heunis


Contact information

Professor Andrew Heunis

Phone: 519-888-4567 x32083

Location: EIT 3115

Fax: 519746-3077

Cross appointed with: Statistics and Actuarial Sciences


  • BSc, Witswaterand, Johannesburg
  • MSc, Imperial College, London

Research interests

  • Stochastic algorithms
  • System identification
  • Nonlinear filtering
  • Stochastic differential equations


  • Heunis, A.J. and Lucic, V.M., "On the innovations conjecture of nonlinear filtering with dependent data",  Elec. J. Prob., v. 13, pp. 2190 - 2216, 2008.
  • Labbe, S.N. and Heunis, A.J., "Convex duality in constrained mean-variance portfolio optimization",  Adv. Appl. Prob., v. 39, pp. 77 - 104, 2007.
  • Hashemi, S.N. and Heunis, A.J., "On the Poisson equation for singular diffusions",  Stochastics, v. 77, pp. 155 - 189, 2005.
  • Heunis, A.J., "Strong  invariance principle for singular diffusions",  Stochastic Processes and their Applications, v. 104, pp. 57 - 80, 2003.
  • Lucic, V.M. and Heunis, A.J., "Convergence  of nonlinear filters for randomly perturbed dynamical systems",  Applied Mathematics and Optimization, v. 48, pp. 93 - 128, 2003.
  • Lucic, V.M. and Heunis, A.J., "On  uniqueness of solutions for the stochastic differential equations of nonlinear filtering",  Annals of Applied Probability, v. 11(1), pp. 182-209, 2001.
  • Joslin, J.A. and Heunis, A.J., "Law   of the iterated logarithm for a constant-gain linear stochastic gradient algorithm",  SIAM Journal on Control and Optimization, v. 39(2), pp. 533-570, 2000.
  • Hashemi, S.N. and Heunis, A.J. "Averaging principle for diffusion processes", Stochastics and Stochastics Reports, v. 62, pp. 201-216, 1998.
  • Pezeshki-Esfahani, H. and Heunis, A.J. "Strong diffusion approximations for recursive stochastic algorithms", IEEE Transactions on Information Theory, v. 43(2), pp. 512-523, 1997.
  • Kouritzin, M.A. and Heunis, A.J. "A law of the iterated logarithms for stochastic processes defined by differential equations with a small parameter," Annals of Probability, v. 22(2) pp. 659-679, 1994.
  • Heunis, A.J. "Rates of convergence for an adaptive filtering algorithm driven by stationary dependent data", SIAM Journal on Control and Optimization, v. 32, pp. 1-24, 1994.
  • Heunis, A.J. and Kouritzin M.A., "Strong convergence in the stochastic averaging principle", to appear in Journal of Mathematical Analysis and Applications.
  • Kouritzin, M.A. and Heunis, A.J. "Rates of convergence in a central limit theorem for stochastic processes defined by differential equations with a small parameter", Journal of Multivariate Analysis, v. 43, pp. 58-109, 1992.
  • Heunis, A.J., "Invariance Principles in parameter estimation", Applied Stochastic Analysis, pp. 537-560, 1991.
  • Heunis, A.J., "On the stochastic differential equations of filtering theory", Journal of Applied Mathematics and Computation, V37, pp. 185-218, 1990.
  • Heunis, A.J., "Asymptotic properties of prediction error estimators in approximate system identification", Stochastics, v. 24, pp. 1-43, 1988.
  • Heunis, A.J. "On the prevalence of stochastic differential equations with unique strong solutions", Annals of Probability, v. 14(2) pp. 653-662, 1987.

Technical reports

Recently Supervised Theses

  • Donnelly, C., "Convex Duality in Mean-variance Portfolio Optimization with a Regime-Switching Model", PhD.
  • Hyndman, C., "Affine Futures and Forward Prices", PhD.
  • Labbe, C., "Contributions to the Theory of Constrained Portfolio Optimization", PhD.
  • Hashemi, S.N., "Singular Perturbations in Coupled Stochastic Differential Equations", PhD.
  • Lucic, V., "On Uniqueness and Weak Convergence of Solutions for the Stochastic Differential Equations of Nonlinear Filtering", PhD.
  • Pezeshki-Esfahani, "Diffusion Approximations for Recursive Stochastic Algorithms", PhD.
  • Joslin, J., "Convergence Properties of the Constant-Gain Adaptive Filtering Algorithm", PhD.
  • Vinke, D., "Quantum Annealing", PhD.
  • Kouritzin, M., "A Study on the Convergence Properties of the Stochastic Averaging Principle", PhD.
  • Smalyanau, A., "The Clarke-Ocone Formula and Optimal Portfolios", MASc., (supervised with R. Mazumdar).
  • Liu, B., "Methods of Convex Analysis in Optimal Control", MASc.
  • Hashemi, S.N., "On the Functional Central Limit Theorem for the Fixed-Gain Robbins-Monro Algorithm", MASc.
  • Joslin, J., "Hypothesis Testing For Markov Chains With General State Space", MASc.
  • Pezeshki-Esfahani, H., "Two Algorithms for the Online Solution of the Wiener-Hopf Equation with A.S. Convergence and Nearly Optimal Rates", MASc.

Current Graduate Students

  • Dian Zhu (PhD)
  • Pradeep Ramchandani (PhD)
  • Alisa Tazhitdinova (MASc)


I have taught the following courses at various times:

  • GE 123 Electrical Engineering (1st year undergraduate; an introduction for students in Chemical, Civil, Environmental and Mechanical Engineering)
  • ECE 304 Numerical Methods (3rd year undergraduate)
  • ECE 316 Probability (3rd year undergraduate)
  • ECE 342 Signals and Systems (3rd year undergraduate)
  • ECE 380 Analogue Control Systems (3rd year undergraduate)
  • ECE 446 Linear Systems; a State-Variable Approach (4th year undergraduate)
  • ECE 685 Stochastic Processes for Dynamical Systems (1st year graduate)
  • ECE 686 Linear Estimation and Stochastic Control (1st year graduate)
  • ECE 784 & STATS 902 Introduction to Stochastic Calculus (2nd year graduate) (course outline, course notes)