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STOCHASTIC MEHLER KERNELS VIA OSCILLATORY PATH INTEGRALS
Truman, Aubrey,Zastawniak, Tomasz Korean Mathematical Society 2001 대한수학회지 Vol.38 No.2
The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schrodinger equation for the harmonic oscillator with a stochastic term of the form (K$\psi$(sub)t)(x) o dW(sub)t, where K is either the position operator or the momentum operator, and W(sub)t is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.