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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).

MSC:

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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