2024/11/27 by Mayer, Matthias Georg
Economics, Econometrics and Finance · #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2411.18555
We give a new characterization for mutual absolute continuity of probability measures on a filtered space. For this, we introduce a martingale limit M that measures the similarity between the tails of the probability measures restricted to the filtration. The measures are mutually absolutely continuous if and only if M = 1 holds almost surely for both measures. In this case, the square roots of the Radon-Nikodym derivatives on the filtration converge in L2. Finally, we apply the result to families of random variables and stochastic processes.