In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any assumptions on the direct feedthrough matrix. We also provide the connection between the stability of the estimator and a system property known as strong detec...

We propose a modeling language for structured specification of interacting components with both hybrid and stochastic dynamics. The behavior of a stochastic hybrid agent is described using a hybrid automaton whose dynamics is specified by stochastic differential equations and probabilistic jumps. Stochastic hybrid agents interact with other agents using shared variables. The operations of paral...

In this paper the basic structure of an integrated approach is discussed that addresses the major conflicts of distributed business process modelling. Our argumentation is grounded on the assumption that process modelling projects of a practically relevant size involve multiple modellers. Current modelling languages and methods, however, do only provide little support for such distributed model...

Asset prices are typically modeled with the geometric Brownian motion (GBM). Correlation between the assets is exogenously modeled and then ad-hoc assigned to the asset prices. This is conceptually and mathematically unsatisfying. We create a new, simple approach, which simultaneously models stochastic volatility and stochastic correlation. This approach replicates the realworld volatility – co...

OF THE DISSERTATION Stochastic Parameterized Grammars: Formalization, Inference and Modeling Applications By Guy Yosiphon Doctor of Philosophy in Computer Science University of California, Irvine, 2009 Professor Eric Mjolsness, Chair The Stochastic Parameterized Grammar (SPG) forms a unifying framework for modeling systems of stochastic nature and dynamical structure. The modeling language is b...

Analytical modeling plays a crucial role in the analysis and design of computer systems. Stochastic Petri Nets represent a powerful paradigm, widely used for such modeling in the context of dependability, performance and performability. Many structural and stochastic extensions have been proposed in recent years to increase their modeling power, or their capability to handle large systems. This...