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Brownian Super-exponents

Probability 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0612160,
  title  = {Brownian Super-exponents},
  author = {Victor Goodman},
  journal= {arXiv preprint arXiv:math/0612160},
  year   = {2007}
}

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10 pages