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Stochastic lie group-valued measures and their relations to stochastic curve integrals, gauge fields and markov cosurfaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1158)

Abstract

We discuss an extension of stochastic analysis to the case where time is multidimensional and the state space is a (Lie) group. In particular we study stochastic group-valued measures and generalized semigroups and show how they can be obtained by multiplicative stochastic integration from vector-valued stochastic Lévy-Khinchin fields. We also discuss their connection to group-valued Markov cosurfaces and, in the case of 2-dimensional "time", group-valued curve integrals. We analyze furthermore, in the general multi-dimensional case, the relation with curve integrals, connections and gauge fields and mention the application of group-valued Markov cosurfaces to the construction of relativistic fields.

Keywords

  • Stochastic Differential Equation
  • Gauge Field
  • Curve Integral
  • Markov Property
  • Markov Semigroup

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1986 Springer-Verlag

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Albeverio, S., Hoegh-Krohn, R., Holden, H. (1986). Stochastic lie group-valued measures and their relations to stochastic curve integrals, gauge fields and markov cosurfaces. In: Albeverio, S.A., Blanchard, P., Streit, L. (eds) Stochastic Processes — Mathematics and Physics. Lecture Notes in Mathematics, vol 1158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080207

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  • DOI: https://doi.org/10.1007/BFb0080207

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