SDEs Driven by SDE Solutions

We consider stochastic differential equations (SDEs) driven by Feller processes which are themselves solutions of multivariate Levy driven SDEs. The solutions of these 'iterated SDEs' are shown to be non-Markovian. However, the process consisting of the driving process and the solution is Markov and even Feller in the case of bounded coefficients. The generator as well as the semimartingale characteristics of this process are calculated explicitly and fine properties of the solution are derived via the stochastic symbol. A short simulation study and an outlook in the direction of stochastic modeling round out the paper.Comment: 16 pages, 9 figure

Glucose Transporter 4 Expression in White Blood Cells of Young and Old Sled Dogs

Obesity has reached alarming levels in the United States Recent statistics show that 1 out of 3 individuals are either obese or overweight! The principle role of the hormone insulin is to mediate the redistribution of the glucose transporter- 4 (Glut4) from an intracellular vesicle pool into plasma membranes of insulin-responsive tissues and thus regulating the uptake of glucose. Insulin resistance is characterized by an inability of cells to respond to insulin upon stimulation with glucose and presents as an important risk factor for the development of type 2 diabetes. Glut4 is the only glucose transporter responsive to insulin and is thought to be found exclusively in muscle an adipose cells. But recently, Maratou et al (2007) demonstrated that there is Glut4 in white blood cells (WBC)collected from human subjects in response to insulin activation. Dogs have been used as a proven biomedical research model for diabetes for over a century since dogs develop insulin dependent and independent forms of diabetes similar to humans. Sled dogs are incredible athletes that provide a homogenous population for studying environmental impacts such as nutrition and exercise on blood parameters. The goal of this study was to 1) develop a protocol to measure Glut4 in white blood cells of sled dogs and 2) compare Glut4 levels in young versus old sled dogs assuming that old sled dogs are at higher risk of diabetes.Nestle Purina partly funded this project

A Classification of Deterministic Hunt Processes with Some Applications

Deterministic processes form an important building block of several classes of processes. We provide a method to classify deterministic Hunt processes. Within this framework we characterize different subclasses (e.g. Feller) and construct some (counter-)examples. In particular the existence of a Hunt semimartingale (on R) which is not an It\^o process in the sense of Cinlar, Jacod, Protter and Sharpe (1980) is proven.Comment: 18 pages, 9 figure

On the Semimartingale Nature of Feller Processes with Killing

Let U be an open set in R^d. We show that under a mild assumption on the richness of the generator a Feller process in U with (predictable) killing is a semimartingale. To this end we generalize the notion of semimartingales in a natural way to those 'with killing'. Furthermore we calculate the semimartingale characteristics of the Feller process explicitly and analyze their connections to the symbol. Finally we derive a probabilistic formula to calculate the symbol of the process directly