We present a self-contained account of recent results on moment identities for Poisson stochastic integrals with random integrands, based on the use of functional transforms on the Poisson space. This presentation relies on elementary combinatorics based on the Faà di Bruno formula, partitions and polynomials, which are used together with multiple stochastic integrals, finite difference operato...

We derive conditional Gaussian type identities of the form E [ exp ( i ∫ T 0 utdBt ) ∣∣∣∣ ∫ T 0 |ut|dt ] = exp ( − 2 ∫ T 0 |ut|dt ) , for Brownian stochastic integrals, under conditions on the process (ut)t∈[0,T ] specified using the Malliavin calculus. This applies in particular to the quadratic Brownian integral ∫ t 0 ABsdBs under the matrix condition A †A2 = 0, using a characterization of Yo...

Dengue Hemorrhagic Fever (DHF) is a tropical disease that always attacks densely populated urban communities. Some factors, such as environment, climate and mobility, have contributed to the spread of disease. The Aedes aegypti mosquito an agent dengue virus in humans, by inhibiting its life cycle it can reduce Therefore, necessary involve dynamics mosquito's model order obtain reliable risk ma...

We consider the problem of computing L1-distances between every pair of probability densities from a given family. We point out that the technique of Cauchy random projections [Ind06] in this context turns into stochastic integrals with respect to Cauchy motion. For piecewise-linear densities these integrals can be sampled from if one can sample from the stochastic integral of the function x 7→...