Nagasawa, Masao; Tanaka, Hiroshi Stochastic differential equations of pure-jumps in relativistic quantum theory. (English) Zbl 0963.81009 Chaos Solitons Fractals 10, No. 8, 1265-1280 (1999). 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). Cited in 1 ReviewCited in 4 Documents 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 Keywords:fractional powers; pure-jump Markov processes; Nagasawa’s stochastic theory PDF BibTeX XML Cite \textit{M. Nagasawa} and \textit{H. Tanaka}, Chaos Solitons Fractals 10, No. 8, 1265--1280 (1999; Zbl 0963.81009) Full Text: DOI References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.