Certain properties related to well posedness of switching diffusions

Hybrid Switching Diffusions : Properties and Applications

Hybrid switching diffusions, also known as switching diffusions or regimeswitching systems, have drawn a signifi cant amount of attention in recent decades in a variety of applications due to their ability to model complex systems with uncertainty. Control and systems engineers have long been familiar with the fundamental idea of using a continuous stochastic differential equation to describe a...

Well-Posedness for a Class of Fourth Order Diffusions for Image Processing

A number of image denoising models based on higher order parabolic partial differential equations (PDEs) have been proposed in an effort to overcome some of the problems attendant to second order methods such as the famous Perona-Malik model. However, there is little analysis of these equations to be found in the literature. In this paper, methods of maximal regularity are used to prove the exi...

Well-Posedness Properties In Variational Analysis And Its Applications

WELL-POSEDNESS PROPERTIES IN VARIATIONAL ANALYSIS AND ITSAPPLICATIONSbyWEI OUYANGAugust 2015Advisor: Prof. Boris S. MordukhovichMajor: Mathematics (Applied)Degree: Doctor of PhilosophyThis dissertation focuses on the study and applications of some significant properties inwell-posedness and sensitivity analysis, among which the notions of uniform metric r...

Ergodic Control of Switching Diffusions*

A bstract . We study the ergodic control problem of switching diffusions representing a typical hybrid system that arises in numerous applications such as fault-tolerant control systems, flexible manufacturing systems, etc. Under fairly general conditions, we establish the existence of a stable, nonrandomized Markov policy which almost surely minimizes the pathwise long-run average cost. We the...

Well-posedness of Hybrid Systems