## Contact information

Email: heunis@uwaterloo.ca

Phone: 519-888-4567 x32083

Location: EIT 3115

Fax: 519746-3077

Cross appointed with: Statistics and Actuarial Sciences

## Education

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

## Research interests

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

## Publications

- 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)

## Teaching

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)