Applications of some formulas for finite Markov chains

Applied and Computational Harmonic Analysis

Volumn 30, Issue 1, 2011, Pages 37-46

  Goldberg, Maxim J ^a   Kim, Seonja ^b  

^a RAMAPO COLLEGE OF NEW JERSEY   (United States)

^b Phyllis Yezzo is the CNO Linda DiDomenico is the director of infection control and Holly Hesse is a nurse currently completing her BSN degree   (United States)

Author keywords

Boundary value problems; Exact expected values for random walks; Feynman Kac formula; Finite Markov chains; Pmf of costs along paths

Indexed keywords

CONTINUOUS PROBLEMS; DISCRETIZATIONS; EXPECTED VALUES; FEYNMAN-KAC FORMULA; FINITE MARKOV CHAIN; FINITE STATE; MARKOV CHAIN; MATRIX FORMULA; MONTE CARLO SIMULATION; PMF OF COSTS ALONG PATHS; PROBABILITY MASS FUNCTION; STOCHASTIC APPROACH;

BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; COSTS; MARKOV PROCESSES; MONTE CARLO METHODS;

RANDOM VARIABLES;

EID: 78649315742     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2010.02.004     Document Type: Article

References (28)

1. R.R. Coifman, and M. Maggioni Diffusion wavelets Appl. Comput. Harmon. Anal. 21 1 July 2006 53 94
2. D.A. Darling, and M. Kac On occupation times for Markov processes Trans. Amer. Math. Soc. 84 1957 444 458
3. R.P. Feynman Space-time approach to nonrelativistic quantum mechanics Rev. Modern Phys. 20 1948 367 387
4. P.J. Fitzsimmons, and J. Pitman Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process Stochastic Process. Appl. 79 1999 117 134
5. I.M. Gel'fand, and A.M. Yaglom Integration in functional spaces and its applications in quantum physics J. Math. Phys. 1 1960 48 69
6. M. Goldberg, S. Kim, Using the pmf of the time to reach a subset of states in an irreducible finite Markov chain for clustering, in: Joint Math. Meetings, AMS Session on Probability and Statistics I, New Orleans, LA, January 5-8, 2007.
7. M. Goldberg, S. Kim, A notion of robust geodesic distance between data points, in: Joint Math. Meetings, AMS Session on Probability, Statistics and Applications II, San Diego, CA, January 6-9, 2008.
8. G.R. Grimmett, and D.R. Stirzaker Probability and Random Processes second edition 1995 Oxford University Press Oxford (reprinted)
9. J.J. Hunter On the moments of Markov renewal processes Adv. in Appl. Probab. 1 1969 188 210
10. J.J. Hunter Generalized inverses and their application to applied probability problems Linear Algebra Appl. 45 1982 157 198
11. J.J. Hunter A survey of generalized inverses and their use in stochastic modelling Res. Lett. Inf. Math. Sci. 1 2000 25 36
12. J.J. Hunter Generalized inverses, stationary distributions and mean first passage times with applications to perturbed Markov chains Res. Lett. Inf. Math. Sci. 3 2002 99 116
13. C.-O. Hwang, and M. Mascagni A Feynman-Kac path-integral implementation for Poisson's equation V.N Alexandrov, Int. Conf. on Computational Science (ICCS 2001) LNCS vol. 2073 2001 Springer-Verlag Berlin 1282 1288
14. C.-O. Hwang, M. Mascagni, and J.A. Given A Feynman-Kac path-integral implementation for Poisson's equation using an h-conditioned Green's function Math. Comput. Simulation 62 2003 347 355
15. C.-O. Hwang, M. Mascagni, and N.A. Simonov Monte Carlo methods for the linearized Poisson-Boltzmann equation Advances in Numerical Analysis 2004 Nova Science Hauppauge, NY
16. M. Kac On the distribution of certain Wiener functionals Trans. Amer. Math. Soc. 65 1949 1 13
17. M. Kac On some connections between probability theory and differential and integral equations J. Neyman, Proc. 2nd Berkeley Symp. Math. Stat. Prob. 1951 Univ. of California Press Berkeley, CA 189 215
18. J.G. Kemeny, and J.L. Snell Finite Markov Chains 1960 Van Nostrand Princeton, NJ
19. G.A. Mikhailov, and B.V. Men'shchikov Solving boundary value problems with complex parameters by the Monte Carlo method Sib. Math. J. 37 4 1996 775 781 translation from Sibirsk. Mat. Zh. 37 4 1996 881 888
20. G.N. Mil'shtejn, and M.V. Tretyakov The simplest random walks for the Dirichlet problem Theory Probab. Appl. 47 1 2002 53 68 translation from Teor. Veroyatn. Primen. 47 1 2002 39 58
21. J.-P. Morillon Numerical solutions of linear mixed boundary value problems using stochastic representations Internat. J. Numer. Methods Engrg. 40 1997 387 405
22. B. ∅ksendal Stochastic Differential Equations: An Introduction with Applications sixth ed. 2007 Springer-Verlag Berlin (corrected fourth printing)
23. J.E. Souza de Cursi Numerical methods for linear boundary value problems based on Feynman-Kac representations Math. Comput. Simulation 36 1 1994 1 16
24. E.M. Stein Topics in Harmonic Analysis Related to the Littlewood-Paley Theory Annals of Mathematics Study vol. 63 1985 Princeton University Press Princeton, NJ (corrected third printing)
25. J. Vigo-Aguiar, R. Ardanuy-Albajar, and B. Wade Stochastic methods for Dirichlet problems J. Math. Model. Algorithms 4 2005 317 330
26. N. Wiener Differential space J. Math. Phys. 2 1923 131 174
27. N. Wiener The average value of a functional Proc. Lond. Math. Soc. Ser. (2) 22 1924 454 467
28. N. Wiener Generalized harmonic analysis Acta Math. 55 1930 117 258