A Geometrical Characterization of Multidimensional Hausdorff Polytopes with Applications to Exit Time Problems

References

• Ang D. D., Gorenflo R., Le V. K., Trong D. D.Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction. Lecture Notes in Math. (2002) 1792(Springer-Verlag, Berlin) Crossref, Google Scholar
• Bhatt A. G., Borkar V. S. Occupation measures for controlled Markov processes: Characterisation and optimality. Ann. Prob. (1996) 24(3):1531–1562Crossref, Google Scholar
• Cho M. J. Linear programming formulation for optimal stopping. (2000) . Ph.D. thesis, The Graduate School, University of Kentucky, LexingtonGoogle Scholar
• Cho M. J., Stockbridge R. H. Linear programming formulation for optimal stopping problems. SIAM J. Control Optim. (2002) 40:1965–1982Crossref, Google Scholar
• Courant R., Hilbert D.Methods of Mathematical Physics (1937) 1Wiley Classics Edition (1989)(John Wiley & Sons, New York) Google Scholar
• Dale A. I. Two-dimensional moment problems. Math. Sci. (1987) 12:21–29Google Scholar
• Decker T. Die Eckpunkte des allgemeinen Dale-Polytopes und ihre Anwendungen in linearen Programmen zur Bestimmung von Austrittszeiten. (2006) . Ph.D. thesis, Humboldt-Universität zu Berlin, BerlinGoogle Scholar
• Ethier S. N., Kurtz T. G.Markov Processes. Characterization and Convergence (1986) (John Wiley & Sons, New York) Crossref, Google Scholar
• Feller W.An Introduction to Probability Theory and Its Applications (1971) 22nd ed.(John Wiley & Sons, New York) Google Scholar
• Hausdorff F. Summationsmethoden und Momentenfolgen. I & II. Math. Z. (1921) 9(74–109):280–299Crossref, Google Scholar
• Hausdorff F. Momentenprobleme für ein endliches Intervall. Math. Z. (1923) 16:220–248Crossref, Google Scholar
• Helmes K., Kall P., Lüthi J.-H. Computing moments of the exit distribution for diffusion processes using linear programming. Oper. Res. Proc. 1998 (1999) (Springer-Verlag, Berlin) 231–240Crossref, Google Scholar
• Helmes K., Pasik-Duncan B. Numerical methods for optimal stopping using linear and non-linear programming. Proc. Workshop “Stochastic Theory and Control,” Lecture Notes in Control and Information Sciences (2002) (Springer-Verlag, Berlin) 185–202Google Scholar
• Helmes K., Stockbridge R. H. Numerical comparison of controls and verification of optimality for stochastic control problems. J. Optim. Theory Appl. (2000) 106:107–127Crossref, Google Scholar
• Helmes K., Stockbridge R. H. Numerical evaluation of resolvents and Laplace transforms of Markov processes. Math. Methods Oper. Res. (2001) 53:309–331Crossref, Google Scholar
• Helmes K., Stockbridge R. H. Extension of Dale's moment conditions with application to the Wright-Fisher model. Stoch. Models (2003) 19(2):255–267Crossref, Google Scholar
• Helmes K., Röhl S., Stockbridge R. H. Computing moments of the exit time distribution for Markov processes by linear programming. Oper. Res. (2001) 49:516–530Link, Google Scholar
• Hernandez-Lerma O., Hennet J. C., Lasserre J. B. Average cost Markov decision processes: Optimality conditions. J. Math. Anal. Appl. (1991) 158:396–406Crossref, Google Scholar
• Hildebrandt T. H., Schoenberg I. J. On linear functional operations and the moment problem for a finite interval in one or several dimensions. Ann. Math. (1933) 34:317–328Crossref, Google Scholar
• Karlin S., Shapley L. S. Geometry of moment spaces. Mem. Amer. Math. Soc. (1953) 12:1–91Google Scholar
• Knight F. B.Essentials of Brownian Motion and Diffusion (1981) (American Mathematical Society, Providence, RI) . Mathematical Surveys No. 18Crossref, Google Scholar
• Knill O. On Hausdorff's moment problem in higher dimensions. (1997) . Preprint, http://www.math.harvard.edu/∼knill/preprints/stability.pdf. Viewed 04/02/2007Google Scholar
• Kurtz T. G., Stockbridge R. H. Existence of Markov controls and characterization of optimal Markov controls. SIAM J. Control Optim. (1998) 36:609–653Crossref, Google Scholar
• Kurtz T. G., Stockbridge R. H. Martingale problems and linear programs for singular control. 37th Ann. Allerton Conf. Comm., Control, and Comput. (1999) (University of Illinois, Urbana-Champaign, IL) 11–20Google Scholar
• Lasserre J. B., Rumeau T. P. SDP vs. LP relaxations for the moment approach in some performance evaluation problems. Stoch. Models (2004) 20:439–456Crossref, Google Scholar
• Manne A. S. Linear programming and sequential decisions. Management Sci. (1960) 6:259–267Link, Google Scholar
• Mendiondo M. S., Stockbridge R. H. Approximation of infinite-dimensional linear programming problems which arise in stochastic control. SIAM J. Control Optim. (1998) 36:1448–1472Crossref, Google Scholar
• Øksendal B.Stochastic Differential Equations (2003) 6th ed.(Springer-Verlag, Heidelberg, Germany) Crossref, Google Scholar
• Riechert S. Ein Vergleich der SDP- mit der LP-Relaxation für die Berechnung optimaler Stoppzeiten. (2004) . Master's thesis, Humboldt-Universität zu Berlin, BerlinGoogle Scholar
• Röhl S. Ein linearer Programmierungsansatz zur Lösung von Stopp- und Steuerungsproblemen. (2001) . Ph.D. thesis, Humboldt-Universität zu Berlin, BerlinGoogle Scholar
• Schwerer E. A linear programming approach to the steady-state analysis of reflected Brownian motion. Stoch. Models (2001) 17:341–368Crossref, Google Scholar
• Shohat J. A., Tamarkin J. D.The Problem of Moments (1943) 1st ed.(American Mathematical Society, Providence, RI) Crossref, Google Scholar
• Stockbridge R. H. Time-average control of martingale problems: A linear programming formulation. Ann. Probab. (1990) 18:206–217Crossref, Google Scholar
• Stockbridge R. H. The problem of moments on a polytope and other bounded regions. J. Math. Anal. Appl. (2003) 285:356–375Crossref, Google Scholar
• Ziegler G. M.Lectures on Polytopes. Graduade Texts in Mathematics (1995) 152(Springer-Verlag, New York) Crossref, Google Scholar