The moments of the area under reflected Brownian bridgeconditional on its local time at zero

[摘要] This paper develops a recursion formula for the conditional moments of the area under the absolute value of Brownian bridge given the local time at 0. The method of power series leads to a Hermite equation for the generating function of the coefficients which is solved in terms of the parabolic cylinder functions. By integrating out the local time variable, this leads to an integral expression for the joint moments of the areas under the positive and negative parts ofthe Brownian bridge.

[学科分类] 应用数学