Final answer:
The Kievan state was overrun in the 13th century during the Mongol invasion led by Genghis Khan, which led to the establishment of the Golden Horde.
Step-by-step explanation:
Asia did not overrun the Kievan state in the 9th, 12th, or 15th centuries. Instead, it was during the 13th century that the Mongol Empire under Genghis Khan invaded the Rus' territories, which included the Kievan Rus', leading to its decline. The Mongol invasion began around 1237 and was part of a larger expansion by the Mongols across Eurasia. The invasion by the Mongols, which was part of their westward expansion across the continent, resulted in the establishment of the Mongol-led Golden Horde in the region once controlled by the Kievan Rus'.