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

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

Author(s) -

Frank B. Knight

Publication year - 1999

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/s1048953300000137

Subject(s) - mathematics , brownian bridge , hermite polynomials , brownian excursion , zero (linguistics) , recursion (computer science) , brownian motion , mathematical analysis , parabolic cylinder function , geometric brownian motion , diffusion process , partial differential equation , parabolic partial differential equation , statistics , knowledge management , linguistics , philosophy , innovation diffusion , algorithm , computer science

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 of the Brownian bridge

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