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
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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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