Large deviations for global maxima of independent superadditive processes with negative drift and an application to optimal sequence alignments

Bernoulli

Volumn 10, Issue 5, 2004, Pages 829-845

  Grossmann, Steffen ^a   Yakir, Benjamin ^b  

^a MAX PLANCK INSTITUTE FOR MOLECULAR GENETICS   (Germany)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Large deviations; Sequence alignment; Superadditive processes

Indexed keywords

EID: 26444458649     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1099579157     Document Type: Article

References (20)

1. Alexander, K.S. (1993) A note on some rates of convergence in first-passage percolation. Ann. Appl. Probab., 3(1), 81-90.
2. Alexander, K.S. (1994) The rate of convergence of the mean length of the longest common subsequence. Ann. Appl. Probab., 4(4), 1074-1082.
3. Alexander, K.S. (1997) Approximation of subadditive functions and convergence rates in limiting-shape results. Ann. Probab., 25(1), 30-55.
4. Arratia, R. and Waterman, M.S. (1994) A phase transition for the score in matching random sequences allowing deletions. Ann. Appl. Probab., 4(1), 200-225.
5. Bundschuh, R. (2002) Rapid significance estimation in local sequence alignment with gaps. J. Comput. Biol, 9, 243-260.
6. Dembo, A., Karlin, S. and Zeitouni, O. (1994a) Critical phenomena for sequence matching with scoring. Ann. Probab., 22(4), 1993-2021.
7. Dembo, A., Karlin, S. and Zeitouni, O. (1994b) Limit distributions of maximal non-aligned twosequence segmental score. Ann. Probab., 22(4), 2022-2039.
8. Durrett, R. (1996) Probability: Theory and Example, 2nd edn. Belmont, CA: Duxbury Press.
9. Feller, W. (1968) An Introduction to Probability Theory and Its Applications, Vol. I, 3rd edn. New York: Wiley.
10. Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. II, 2nd edn. New York: Wiley.
11. Grossmann, S. (2003) Statistics of optimal sequence alignments. Doctoral thesis, Johann Wolfgang Goethe University, Frankfurt. Available at http://publikationen.stub.uni-frankfurt.de/volltexte/2003/292/.
12. Hammersley, J.M. (1974) Postulates for subadditive processes. Ann. Probab., 2(4), 652-680.
13. Kingman, J.F.C. (1975) Subadditive processes. In EL. Hennequin (éd.), École d'Eté de Probabilités de Saint-Flour V, Lecture Notes in Math. 539, pp. 167-223. Berlin: Springer-Verlag.
14. Mott, R. (2002) Accurate formula for p-vaIues of gapped local sequence and profile alignments. J. Mol. Biol., 300, 649-659.
15. Rockafellar, R.T. (1979) Convex Analysis. Princeton, NJ: Princeton University Press.
16. Siegmund, D. and Yakir, B. (2000) Approximate p-values for local sequence alignments. Ann. Statist., 28(3), 657-680.
17. Spitzer, F. (1976) Principles of Random Walks, 2nd edn. Springer, New York: Springer-Verlag.
18. Steele, J.M. (1997) Probability Theory and Combinatorial Optimization. Philadelphia: Society for Industrial and Applied Mathematics.
19. Waterman, M.S. and Vingron, M. (1994) Sequence comparison significance and Poisson approximation, Statist. Sci., 9(3), 367-381.
20. Zhang, Y. (1995) A limit theorem for matching random sequences allowing deletions. Ann. Appl. Probab., 5(4), 1236-1240.