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Kalinichenko, A. A.

Construction of Levi processes on path spaces of Lie groups. (English) Zbl 1335.60074

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19, No. 1, Article ID 1650002, 22 p. (2016).
Summary: Given a compact Lie group and a conjugate-invariant Levi process on it, generated by the operator \((L,D(L))\), we construct the Levi process on the path space of \(G\), associated with the convolution semigroup \(\{\mu_t:t\geq0\}\) of probability measures, where \(\mu_t\) is the distribution of the Levi process on \(G\) generated by \((tL,D(L))\). The constructed process is obtained as the weak limit of piecewise constant paths, which, as well as proving its existence and properties, provides finite-dimensional approximations of Chernoff type to the integrals with respect to its distribution.

MSC:

60G51 Processes with independent increments; Lévy processes
60F17 Functional limit theorems; invariance principles
60F05 Central limit and other weak theorems
60J65 Brownian motion
60J60 Diffusion processes

Keywords:

Lévy processes; Lie groups; path spaces; Brownian sheet; functional integration
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References:

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