The Minkowski equality of filtrations

On the Equality Conditions of the Brunn-minkowski Theorem

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality. The Brunn-Minkowski Theorem asserts that, for compact convex sets K,L ⊆ Rn, the n-th root of the Euclidean volume Vn is concave with respect to Minkowski combinations; that is, for λ ∈ [0, 1], Vn((1− λ)K + λL) ≥ (1− λ)Vn(K) + λVn(L). The equality condition asserts that if K and L both have positive ...

The Brunn-Minkowski-Type Inequality

Carthaginian Enlargement of Filtrations ∗ . †

In this work, we revisit some well-known results in the theory of initial and progressive enlargement of a reference filtration F with a random time τ , providing, under an equivalence assumption slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to the already existing ones. We also characterize martingales in the enlarged filtrations in terms of martingales...

Enlargements of Filtrations

the effect of taftan pozzolan on the compressive strength of concrete in the environmental conditions of oman sea (chabahar port)

cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...