Brownian Super-exponents

Details Brownian Super-exponents Brownian Super-exponents

2006-12-06

arxiv.org/abs/math/0612160v1

Mathematics

Probability

10 pages

Scientific paper

We introduce a transform on the class of stochastic exponentials for d-dimensional Brownian motions. Each stochastic exponential generates another stochastic exponential under the transform. The new exponential process is often merely a supermartingale even in cases where the original process is a martingale. We determine a necessary and sufficient condition for the transform to be a martingale process. The condition links expected values of the transformed stochastic exponential to the distribution function of certain time-integrals.

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