A. Markov published several papers on his chains, starting in 1906, so it is written, in the journal:
(1) Извѣстія Физико-математического общества при Казанском университете
I am surprised by the difficulty of finding the papers to read, surprised because of just how well-know this material is today. The only work by Markov I can find is his 1900 book "Calculating Variation" and an earlier book in German.
The journal (1) still exists today, having published without interruption. They have back issues available, but only for the last decade. They have an archive 1834-2014! It consists of important papers and is a WIP. Ah, I see, Markov's work is apparently not sufficiently important (because it's not there), although a paper by his son without mathematical content is.
1a) Did Markov invent the concept of Markov chains? I ask whomever had read his papers, not ABOUT his papers. 1b) Was the general idea—if not the various theorems proved using the approach—know earlier, perhaps by Karl Pearson (or William Clifford) or John Strutt. 1c) If you did read Markov's papers, where are they available, at least the 15th volume, if not the later or earlier volumes? (My university, for instance, has a great Imperial and Soviet collection, but not this; it may be obscure.) If the papers might be in some paywall database, not necessarily scanned and archived, please suggest where to look; I have access probably.
2) What influential papers began the use of Markov chains outside the USSR? I presume this occurred in the 1920's. Because the use of such concepts in the ergodic context came soon after, I know having read those papers.
3) What are the OLDEST papers of important results proved using Markov chains in $\mathbb{C}^n$?
EDIT A: Following the suggestions in the answers below I found links to both volumes of collected works:
http://publ.lib.ru/ARCHIVES/M/MARKOV_Andrey_Andreevich/_Markov_A.A..html
EDIT B: The attribution of Markov's paper, Распространение закона больших чисел на величины, зависящие друг от друга, the usually cited origin of Markov chains, to (1) in the year 1906, volume 15(4),135-156, is strange. In the collected works, it's dated by Markov: 25 March 1907, apparently this being the final version printed in 1907 as a booklet.
Best Answer
Obtaining old issues of this journal is difficult, though perhaps some American libraries have it, and you can try Interlibrary Loan (ILL). Alternatively, there are two volumes of collected papers Markov's Collected papers, MR0050525 the papers you are looking for must be in this volume. Our library has this, so you can surely obtain this via ILL.
BTW, historians say that Markov chains were introduced for the first time in his paper of 1913, here is an account available online:
http://www.americanscientist.org/libraries/documents/201321152149545-2013-03Hayes.pdf
It gives a reference to an English translation which must be easily available. Also: http://www.alpha60.de/research/markov/ which has links to some translations.
Here is one of the papers you are asking: http://www.alpha60.de/research/markov/DavidLink_OnARemarkableCase_MarkovTrans_2007.pdf