Who are some famous USSR/Russian Statistics/probability academic researchers? Who are some famous USSR/Russian Statistics/probability academic researchers?  Are russian (current Russia and former USSR) strong in this field academically?
 A: It is hard to underestimate the contribution of Andrey Kolmogorov, for putting probability theory on a rigorous mathematical footing during the Soviet era.
Also, Andrey Markov, for his contribution to stochastic processes and Markov chains in particular, though most of his work was in the pre-Soviet era.
Possibly worth mentioning, though he was pre-Soviet Russia, Pafnuty Chebyshev for the Chebyshev inequality.
A: Vladimir Vapnik - important contributions to computational learning theory (e.g. VC theory) and an inventor of the support vector machine.
A: As @PSellaz mentions, Kolmogorov's contributions are very fundamental and include the standard axiomatization of the notion of probability (there are other ways to define a probability, but they aren't as well known as Kolmogorov's definition.) You might have also heard of Kolmogorov-Smirnov test and Kolmogorov's 0-1 Theorem.  Due to his influence, there was a Soviet school of probability during the Soviet years. Some of Kolmogorov's students became well-known probability theorists. Yakov Sinai (currently in Princeton) is one of them. Yuri Prokhorov and Eugene Dynkin are two others. The American Mathematical Society has for many years translated the journal Theory of Probability and Mathematical Statistics from Russian into English. The list of editors and contributors should give you a good idea of who the current players are. To get an idea of how things were during Kolmogorov's time, look at Paul Halmos's book I Want to Be a Mathematician.
A: USSR was strong in both probability and statistics, but after breakdown of USSR many of the most prominent scientists leaved Russia and have worked during a long term in Western Universities. However, some of them now work partially in Russia. 
I don't say that I mention all of prominent statistics with deep connection with Russia, I just provide a list of people I encountered. Order is alphabetic.


*

*Golubev - now works on oracle inequalities for linear regression.

*Shiryaev - one of the most widely known Russian scientists, disciple of the Kolmogorov probability school. He has prominent results in almost all probabily-related fields.

*Spokoiny - now he is on the cutting edge of modern statistics, works mostly in Germany now.

*Tsybakov - well-known statistics with h index as large as 28 according to the Microsoft Academics search. I visited his lectures on sparsity in statistics. Works in France.

