Stochastic maps, continuous approximation, and stable distribution

Approximation of Stable and Geometric Stable Distribution

Although there has been increased interest in the application of the stable and geometric stable distributions in economics and finance, further application has been limited because their probability density function does not have an explicit solution. In this paper, we present three analytic approximation methods — homotopy perturbation method, Adomian decomposition method, and variational ite...

Relative Compactness and Product Stable Quotient Maps

Combination of Approximation and Simulation Approaches for Distribution Functions in Stochastic Networks

This paper deals with the fundamental problem of estimating the distribution function (df) of the duration of the longest path in the stochastic activity network such as PERT network. First a technique is introduced to reduce variance in Conditional Monte Carlo Sampling (CMCS). Second, based on this technique a new procedure is developed for CMCS. Third, a combined approach of simulation and ap...

Continuous approximation schemes for stochastic programs

One of the main methods for solving stochastic programs is approximation by discretizing the probability distribution. However, discretization may lose differentiability of expectational functionals. The complexity of discrete approximation schemes also increases exponentially as the dimension of the random vector increases. On the other hand, stochastic methods can solve stochastic programs wi...

Continuous, Stable, and Linear Maps of Coherence Spaces

One can check that there exists a coherent space which is finite. Let us observe that a set is binary complete if: (Def.1) For every set A such that for all sets a, b such that a ∈ A and b ∈ A holds a ∪ b ∈ it holds ⋃ A ∈ it. Let X be a set. The functor FlatCoh(X) yielding a set is defined as follows: (Def.2) FlatCoh(X) = CohSp(△X). The functor SubFin(X) yielding a subset of X is defined by: (D...