ANOVA for diffusions and Itô processes

Anova for Diffusions and Ito Processes

Ito processes are the most common form of continuous semimartingales, and include diffusion processes. The paper is concerned with the nonparametric regression relationship between two such Ito processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic v...

A Useful Family of Stochastic Processes for Modeling Shape Diffusions

 One of the new area of research emerging in the field of statistics is the shape analysis. Shape is defined as all the geometrical information of an object whose location, scale and orientation is not of interest. Diffusion in shape analysis can be studied via either perturbation of the key coordinates identifying the initial object or random evolution of the shape itself. Reviewing the f...

Stochastic Processes and Control for Jump-Diffusions∗

An applied compact introductory survey of Markov stochastic processes and control in continuous time is presented. The presentation is in tutorial stages, beginning with deterministic dynamical systems for contrast and continuing on to perturbing the deterministic model with diffusions using Wiener processes. Then jump perturbations are added using simple Poisson processes constructing the theo...

On Fliess operators driven by L2-Itô random processes

Fliess operators with deterministic inputs have been studied since the late 1970’s and are well understood. When the inputs are stochastic processes the theory is less developed. There have been several interesting approaches for Wiener process inputs. But the interconnection of systems is not well-posed in this context, and this limits their use in applications. This paper has two specific goa...

Controlled Switching Diffusions as Hybrid Processes