Stochastic Mehler kernels via oscillatory path integrals

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JournalJournal of the Korean Mathematical Society
DatePublished - 2001
Issue number2
Volume38
Number of pages14
Pages (from-to)469-483
Original languageEnglish

Abstract

The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schr¨odinger equation for the harmonic oscillator with a stochastic term of the form (K t)(x) dWt, where K is either the position operator or the momentum operator, and Wt is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.

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