Brownian super-exponents

Victor Goodman
2007 Communications on Stochastic Analysis  
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
more » ... tial to the distribution function of certain time-integrals. 2000 Mathematics Subject Classification. 60H30; 60J65.
doi:10.31390/cosa.1.1.11 fatcat:smn4wwwlifhybac2ro7klzpdea