On Path Integrals for the High-Dimensional Brownian Bridge

Details On Path Integrals for the High-Dimensional Brownian Bridge On Path Integrals for the High-Dimensional Brownian Bridge

2004-04-02

arxiv.org/abs/math/0404047v1

J. Comput. Appl. Math., 44, 381 - 390 (1992)

Mathematics

Probability

13 pages

Scientific paper

Let v be a bounded function with bounded support in R^d, d>=3. Let x,y in 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->infty, 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.

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