Some remarks on absolute continuity and quantization of probability measures

Absolute Continuity and Singularity of Probability Measures in Functional Spaces

Some Remarks on Absolute Mathematics

We calculate Hochschild cohomology groups of the integers treated as an algebra over so-called ”field with one element”. We compare our results with calculation of the topological Hochschild cohomology groups of the integers this is the case when one considers integers as an algebra over the sphere spectrum.

Probability Structure Preserving and Absolute Continuity ✩

– The concept of probability structure preserving mapping is introduced. The idea is applied to define stochastic integral for fractional Brownian motion (fBm) and to obtain an anticipative Girsanov theorem for fBm.  2002 Éditions scientifiques et médicales Elsevier SAS AMS classification: 60H05; 60H07; 60H15; 60B11; 28B20

Some Remarks on Output Measures

An output measure is an image of a uniform Bernoulli measure on finitely many states. We discuss “generalized Bernoulli” measures of [F-J], and answer several questions posed in that paper, in particular we establish a condition when such a measure is a finitary output measure. Answering D. Goldstein’s question, we characterize output measures via block codes in terms of walks on labeled graphs...

Some Remarks on the Probability of Cycles

Standard results suggest that the probability of cycles should increase as the number of options increases and also as the number of individuals increases. These results are, however, premised on a so-called "impartial culture" assumption: any logically possible preference ordering is assumed to be as likely to be held by an individual as any other. The present chapter shows, in the three-optio...