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Exact formulas of certain functional integrals on Wiener spaces. (English) Zbl 0832.60048

Summary: An elementary method is used to derive formulas of the form \(E_w [\exp z (\langle Ax, x \rangle + \langle h,x \rangle)]\) on an abstract Wiener space \((H,B,W)\). Here \(h \in H\), \(A\) is a trace class operator on \(H\) and \(z\) is a complex number satisfying \(\sup_{|h |_H = 1} \text{Re} z \langle Ah, h \rangle_H < 1\). Some explicit examples including Lévy’s stochastic area formula are given to illustrate how to implement this simple method.

MSC:

60G15 Gaussian processes
60G35 Signal detection and filtering (aspects of stochastic processes)
60J65 Brownian motion
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