Onishchik A. A. Kirillov and E. B. Vinberg who obtained their first results on Lie groups in
Dynkin's seminar. At a later stage the work of the seminar was greatly enriched by the active
participation of 1. 1. Pyatetskii Shapiro. As already noted Dynkin started to work in
probability as far back as his undergraduate studies. In fact his first published paper deals
with a problem arising in Markov chain theory. The most significant among his earliest
probabilistic results concern sufficient statistics. In [15] and [17] Dynkin described all
families of one-dimensional probability distributions admitting non-trivial sufficient
statistics. These papers have considerably influenced the subsequent research in this field.
But Dynkin's most famous results in probability concern the theory of Markov processes.
Following Kolmogorov Feller Doob and Ito Dynkin opened a new chapter in the theory of Markov
processes. He created the fundamental concept of a Markov process as a family of measures
corresponding to var ious initial times and states and he defined time homogeneous processes
in terms of the shift operators ()t. In a joint paper with his student A.
