Martin V. Day - Research Publications

Where available, links are to preprints (i.e. preliminary draft versions) in pdf format.  In some cases the preprints may include errors or other material which was edited out in the published versions. See the published journals for the actual final versions.

Papers on the Small Parameter Exit Problem

• Exponential Leveling for Stochastically Perturbed Dynamical Systems, SIAM J. Math. Anal. 4 (1982) pp. 532-540.
• On the Exponential Exit Law on the Small Parameter Exit Problem, Stochastics 8 (1983), pp. 297-323.
• On the Asymptotic Relation between Equilibrium Density and Exit Measure in the Exit Problem, Stochastics 12 (1984), pp. 303-330.
• Some Regularity Results on the Ventcel-Freidlin Quasi-Potential Function (co-authored with Tom Darden), Appl. Math Opt. 13 (1985), pp. 259-282.
• The Exterior Sphere condition for the Ventcel-Freidlin Quasi-Potential Function, Appl. Math Opt. 14 (1986), pp. 49-54.
• Recent Progress on the Small Parameter Exit Problem, Stochastics 20, (1987), pp. 121-150.
• Localization Results for Densities Associated with Stable Small-Noise Diffusions, Prob. Th. and Rel. Fields 77 (1988), pp. 457-470.
• Boundary Local Time and Small Parameter Exit Problems with Characteristic Boundaries, SIAM J. Math. Anal. 20 (1989), pp. 222-248.
• Large Deviations Results for the Exit Problem with Characteristic Boundary, J. Math. Anal. and Appl. 147 (1990), pp. 134-153.
• Some Phenomena of the Characteristic Boundary Exit Problem, Diffusion Processes and Related Problems in Analysis, Volume 1, pp. 55-72, Birkhäuser, Boston, 1990.
• Conditional Exits for Small Noise Diffusions with Characteristic Boundary, Annals of Probability 20 (1992), pp. 1385-1419.
• Regularity of Boundary Quasipotentials for Planar Systems, Appl. Math. Opt. 30 (1994), pp. 79-101.
• Cycling and Skewing of Exit Measures for Planar Systems, Stochastics 48 (1994), pp. 227-247.
• On the Exit Law from Saddle Points, StochasticProcesses and their Applications 60 (1995), pp. 287-311.
• Exit Cycling for the Van der Pol Oscillator and Quasipotential Calculations, J. Dynamics and Differential Equations 8 (1996), pp. 573-601.
• Mathematical Approaches to the Problem of Noise Induced Exit., in Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W. H. Fleming, (W. M. McEneaney, G. G. Yin and Q. Zhang, eds.), Birkhauser, Boston, 1999.

Papers Related to Queueing Theory and Queueing Motivated Differential Games

• Robust L2-Gain Control for Nonlinear Systems With Projection Dynamics and Input Constraints: An Example From Traffic Control (co-authored with J. Ball, T. Yu and P. Kachroo), Automatica 35  (1999), pp. 429-444.
• Robust Feedback Control of a Single Server Queueing System (co-authored with J. A. Ball and P. Kachroo), Mathematics of Control, Signals and Systems 12 (1999) pp. 307-345.
• Robust Optimal Stopping-time Control for Nonlinear Systems (co-authored with J. A. Ball and J. Chudoung), Appl. Math. & Optimization 46 (2002), pp. 1-29.
• Robust Optimal Switching Control for Nonlinear Systems (co-authored with J. A. Ball and J. Chudoung), SIAM J. Control and Optimization 41 (2002), pp. 900-931.
• Robust Optimal Service Analysis of Single-Server Re-Entrant Queues (co-authored with J. Hall, J. Menendez, D. Potter, and I Rothstein), Computational Optimization and Applications 22 (2002), pp. 261-302.
• Boundary-Influenced Robust Controls: Two Network Examples, ESAIM: Control, Optimisation and Calculus of Variations, 12 (2006), pp. 662-698.
• On the Velocity Projection for Polyhedral Skorokhod Problems, Applied Mathemaics E-Notes 5 (2005), pp. 52-59.
• On Neumann type Boundary Conditions for Hamilton-Jacobi Equations in Smooth Domains, Appl. Math. & Optimization, 5 (2006), pp.359-381. (The published version is available at http://www.springerlink.com.)
• Fluid Limits of Optimally Controlled Queueing Networks (co-authored with G. Pang), Journal of Applied Mathematics and Stochastic Analysis, ,vol. 2007, Article ID 68958, 19 pages, 2007. doi:10.1155/2007/68958.
  
• Simple Singularities for Max-Concave Hamilton-Jacobi Equations and Generalized Characteristics (co-authored with Arik Melikyan), J. Optimization Theory and Applications, 138 (2008), pp. 155-174.  (The published version is available at http://www.springerlink.com.)
• A Uniqueness Result for p-Monotone Viscosity Solutions of Hamilton-Jacobi Equations in Bounded Domains, SIAM J. Control and Optimization 47 (2009), pp. 3167-3184.
• Weak Convergence and Fluid Limits in Optimal Time-to-Empty Queueing Control Problems, Appl. Math. & Optimization, vol. 64 (2011), pp. 339-362.
• A Characterization of the Reflected Quasipotential (co-authored with Kasie Farlow), Appl. Math. & Optimization, vol. 72 (2015), pp. 435-468.

Papers on Miscellaneous Topics

• On a Stochastic Control Problem with Exit Constraints, Appl. Math. Opt. 6 (1980), pp. 181-188.
• Discount Optimality throughout a Set of Parameters for One-Dimensional Transport Processes Z. Wahr. 56 (1981), pp. 515-530.
• Comparison Results for Diffusions Conditioned on Positivity, J. of Appl. Prob. 20 (1983), pp. 766-777.
• Derivative Estimates for Eigenfunctions with Accessible Boundaries and Application to Diffusions, Applicable Analysis 16 (1983), pp. 329-344.
• Characteristic characterization of viscosity supersolutions corresponding to nonlinear H∞ control (co-authored with W. M. McEneaney), Proc. 13th IFAC World Congress, Vol.E (1996), pp.401-406.
  
• On Lagrange Manifolds and Viscosity Solutions (summary), J. Math. Systems, Estimation and Control 8 (1998), pp. 369-372.
• Book Review: Functional Integration and Partial Differential Equations, by M. Freidlin, Bulletin of the AMS 17 (1987), pp. 346-351.