Stochastic differential equations of pure-jumps in relativistic quantum theory. (English) Zbl 0963.81009

Summary: The movement of relativistic quantum particles is described with pure-jump Markov processes in Nagasawa’s stochastic theory. Markov processes of pure-jumps are characterized in terms of stochastic differential equations of pure-jumps. The existence and uniqueness of solutions of stochastic differential equations of pure-jumps are shown under some regularity conditions. Markov processes of pure-jumps are then constructed with the help of the Schrödinger representation (process).


81P20 Stochastic mechanics (including stochastic electrodynamics)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
81S25 Quantum stochastic calculus
60K40 Other physical applications of random processes
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