Stochastic mappings and random distribution fields: A correlation approach

Stochastic Processes and Random Fields

Strata of Random Mappings – a Combinatorial Approach

Let Fn denote the set of all mappings φ : {1, . . . , n} → {1, . . . , n} and assume that this set is equipped with the uniform distribution. Then a mapping φ ∈ Fn is usually called a random mapping. For our investigations it is convenient to represent random mappings by its functional graph Gφ, i.e. the graph consisting of the nodes 1, 2, . . . , n and of the edges (i, φ(i)), i = 1, . . . , n....

Random Fields and Stochastic Geometry (09w5040)

The main topics of this workshop lay at the point where Probability meets Geometry, specifically the study of the random geometry and topology generated by smooth random functions. While these problems have their roots in various applications of image and shape analysis in a wide variety of disciplines, their main mathematical content lies in probability theory. It is there that recent major ad...

From Random Processes to Generalized Fields: a Unified Approach to Stochastic Integration

The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic integrands. The problem is then to extend the definition to random integrands. An orthogonal decomposition of chaos space of the random field leads to two suc...

A stochastic approach to nonlinear unconfined flow subject to multiple random fields

In this study, the KLME approach, a momentequation approach based on the Karhunen–Loeve decomposition developed by Zhang and Lu (Comput Phys 194(2):773–794, 2004), is applied to unconfined flow with multiple random inputs. The log-transformed hydraulic conductivity F, the recharge R, the Dirichlet boundary condition H, and the Neumann boundary condition Q are assumed to be Gaussian random field...