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- Krishna B. Athreya, John M. Hitchcock, Jack H. Lutz, Elvira Mayordomo
- SIAM J. Comput.
- 2004

The two most important notions of fractal dimension are Hausdorff dimension, developed by Hausdorff (1919), and packing dimension, developed independently by Tricot (1982) and Sullivan (1984). Both dimensions have the mathematical advantage of being defined from measures, and both have yielded extensive applications in fractal geometry and dynamical… (More)

We postulate that {Zn} satisfy the recurrence relations (5) E(s^\Fn,z) = K W ] ^ a.s. and for any set of integers l ^ W i < w 2 < • • • <rik with | s t | â l , A MS Subject Classifications. Primary 6067; Secondary 6030.

The Markov chain simulation method has been successfully used in many problems, including some that arise in Bayesian statistics. We give a self-contained proof of the convergence of this method in general state spaces under conditions that are easy to verify.

The two most important notions of fractal dimension are Hausdorff dimension, developed by Hausdorff (1919), and packing dimension, developed independently by Tricot (1982) and Sullivan (1984). Both dimensions have the mathematical advantage of being defined from measures, and both have yielded extensive applications in fractal geometry and dynamical… (More)

- Krishna B. Athreya
- J. Applied Probability
- 2012

- Krishna B. Athreya, C. R. Pranesachar, Navin M. Singhi
- Eur. J. Comb.
- 1980

Let {Y :n ~ o} be a Harris-recurrent Markov chain on a general state n space. It is shown that {Y J is strong mixing, provided there exists a n stationary probability distribution ~(.) for {Y}. We use this result to n establish that certain stationary autoregressive moving average processes are strong mixing. Necessary and sufficient conditions for a first… (More)

- Krishna B. Athreya
- Journal of mathematical biology
- 1992

If qk is the extinction probability of a slightly supercritical branching process with offspring distribution [pkr:r = 0, 1, 2, ...], then it is shown that if supk sigma r r3pkr less than infinity, inf sigma 2k greater than 0, and mk----1, then 1-qk approximately 2(mk - 1)sigma -2k, where mk = sigma r rpkr, sigma 2k = k sigma r r2pkr - m2k. This provides a… (More)

Some growth asymptotics of a version of ‘preferential attachment’ random graphs are studied through an embedding into a continuous-time branching scheme. These results complement and extend previous work in the literature.

Let {Xn : n = 0, 1, 2, ...} be a real-valued Markov chain. The purpose of this paper is to study properties of kernel type estimators of the stationary density and of the transition density of such a chain. These estimators were considered first by Roussas (1969) and by Rosenblatt (1970). Both authors extended to the Markov chain case some results for… (More)