2006/12/06 by Goodman, Victor
#60H30 #60J65 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.math/0612160
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.