Feynman approximation to integrals with respect to Brownian sheet on Lie groups. (English) Zbl 1322.60080

Kalinichenko, A. A.

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18, No. 1, Article ID 1550008, 15 p. (2015).

Summary: We consider the Feynman-type approximations to functional integrals over the distribution of the Brownian sheet on a compact connected Lie group \(M\), which give a representation of the integrals over the functional space \(C([0, 1] \times [0, 1]\), \(M\)) as the limit of integrals over the finite-dimensional manifolds \(M \times \cdots \times M\). The known approximation formulas for the one-parameter Brownian motion are generalized to the case of the Brownian sheet.

MSC:

60H05	Stochastic integrals
60G60	Random fields

Keywords:

functional integration; Brownian sheet; Feynman approximation; Lie groups

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