Stockman was born on July 21, 1947, in Kharkiv, Ukrainian Soviet Socialist Republic to a Jewish family with Cantonist roots.
[1] Stockman completed his secondary education at the Republican Specialized Physics and Mathematics Boarding School in Kyiv.
He completed his PhD at Institute of Nuclear Physics in Novosibirsk in 1974 under the supervision of Spartak Belyaev and Vladimir Zelelevinsky.
[1] No longer being interested in nuclear physics, Stockman transferred to the Institute of Automation and Electrometry in Novosibirsk following his PhD and started working on nonlinear optics as a research scientist under the supervision of Sergey Rautian.
[2] Stockman also held visiting positions at Max Planck Institute of Quantum Optics, University of Stuttgart, École normale supérieure Paris-Saclay and ESPCI Paris.