If you need an accessible version of this item please contact JSTOR User Support

Limit Distributions of Maximal Segmental Score among Markov-Dependent Partial Sums

Samuel Karlin and Amir Dembo
Advances in Applied Probability
Vol. 24, No. 1 (Mar., 1992), pp. 113-140
DOI: 10.2307/1427732
Stable URL: http://www.jstor.org/stable/1427732
Page Count: 28
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Limit Distributions of Maximal Segmental Score among Markov-Dependent Partial Sums
Preview not available

Abstract

Let s1,⋯ ,sn be generated governed by an r-state irreducible aperiodic Markov chain. The partial sum process Sα ,m=∑i=0 m-1Xsi,si+1 , m=1,2,⋯ is determined by a realization {si}i=0 n of states with s0=α and the real-valued i.i.d. bounded variables Xα β associated with the transitions si=α, si+1=β . Assume Xα β has negative stationary mean. The explicit limit distribution of the maximal segmental sum Mα(n)=max0≤ k≤ l≤ n[Sα ,l-Sα ,k] is derived. Computational methods with potential applications to the analysis of random Markov-dependent letter sequences (e.g. DNA and protein sequences) are presented.

Page Thumbnails

  • Thumbnail: Page 
113
    113
  • Thumbnail: Page 
114
    114
  • Thumbnail: Page 
115
    115
  • Thumbnail: Page 
116
    116
  • Thumbnail: Page 
117
    117
  • Thumbnail: Page 
118
    118
  • Thumbnail: Page 
119
    119
  • Thumbnail: Page 
120
    120
  • Thumbnail: Page 
121
    121
  • Thumbnail: Page 
122
    122
  • Thumbnail: Page 
123
    123
  • Thumbnail: Page 
124
    124
  • Thumbnail: Page 
125
    125
  • Thumbnail: Page 
126
    126
  • Thumbnail: Page 
127
    127
  • Thumbnail: Page 
128
    128
  • Thumbnail: Page 
129
    129
  • Thumbnail: Page 
130
    130
  • Thumbnail: Page 
131
    131
  • Thumbnail: Page 
132
    132
  • Thumbnail: Page 
133
    133
  • Thumbnail: Page 
134
    134
  • Thumbnail: Page 
135
    135
  • Thumbnail: Page 
136
    136
  • Thumbnail: Page 
137
    137
  • Thumbnail: Page 
138
    138
  • Thumbnail: Page 
139
    139
  • Thumbnail: Page 
140
    140