Strategy Page provides some background on the possibility of conflict on the Caspian in the post-Soviet era:
The Caspian Sea, long a Russian lake, is now witnessing a naval arms race. Before the Soviet Union broke up in 1991, the only nations bordering the Caspian were Russia (with most of the coastline) and Iran. But now those two nations have been joined by parts of the Soviet Union that have become independent states (Kazakhstan, Azerbaijan and Turkmenistan). It goes downhill from there.
Iran shares a land border with Azerbaijan and has a historical claim on Azerbaijan. In the 19th century Azerbaijan (as in the area occupied the Azeris, a Turkic people) was divided by Russia and Iran. Currently about a quarter of the Iranian population is Azeri, but the Azeris of Azerbaijan believe all Azeris should be part of an independent Azerbaijan. This was how it was for centuries before Turkey, Russia and Iran began seeking to conquer Azerbaijan. Some Iranian Azeris like this idea and Iran is always looking for ways to make Azerbaijan back off. So Iran is building up its Caspian naval forces, which is annoying Russia more than Azerbaijan.
The Iranian buildup includes a new corvette, an Iranian built 1,400 ton ship. Azerbaijan responded by buying $1.6 billion worth of weapons from Israel (which angered Iran a great deal.) Among the items ordered were Gabriel anti-ship missiles. These are 522 kg (1,150 pound) weapons with a range of 36 kilometers. Azerbaijan will use these to protect its Caspian Sea coast from the growing number of Iranian warships being introduced in the area. Most of the Iranian Caspian “fleet” consists of small patrol boats. Some are armed with anti-ship missiles but they are basically coast guard type craft.
What really controls the Caspian is aircraft and Russia has the most of those. Russia also has the only water link to the ocean and thus the ability to bring in more warships on short notice. These, plus Russia’s larger air force gives Russia the edge.