Journal of the
Korean Mathematical Society JKMS

The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schr\"{o}dinger equation for the harmonic oscillator with a stochastic term of the form $(K\psi_{t})(x)\circ dW_{t}$, where $K$ is either the position operator or the momentum operator, and $W_{t}$ is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.

Keywords: Stochastic Schr{o}dinger equation, path integrals, Mehler kernel

MSC numbers: 60H15, 81S40, 81S30