ON PATH-INTEGRALS FOR THE HIGH-DIMENSIONAL BROWNIAN BRIDGE

[摘要] Let v be a bounded function with bounded support in R(d), d greater-than-or-equal-to 3. Let x, y is-an-element-of R(d). Let Z(t) denote the path integral of v along the path of a Brownian bridge in R(d) which runs for time t, starting at x and ending at y. As t --> infinity, it is perhaps evident that the distribution of Z(t) converges weakly to that of the sum of the integrals of v along the paths of two independent Brownian motions, starting at x and y and running forever. Here we prove a stronger result, namely convergence of the corresponding moment generating functions and of moments. This result is needed for applications in physics.

[发布日期] 1992-12-24

[关键词] FEYNMAN-KAC FORMULA;MOMENT GENERATING FUNCTION;METHOD OF MOMENTS;STATISTICAL MECHANICS;SCHRODINGER EQUATION;GREEN FUNCTION