The Construction of a Class of Measure-valued Processes of Stochastic Flows

In this article, we give a description of measure-valued processes with interactive stochastic flows. It is a unified construction for superprocesses with dependent spatial motion constructed by Dawson, LI, Wang and superprocesses of stochastic flows constructed by Ma and Xiang.

CONTINUITY OF l^2-VALUED TWO-PARAMETER ORNSTEIN UHLENBECK PROCESSES

Let {Y (t);t= (t 1,t 2)≥0}={X k(t 1,t 2);t 1≥0,t 2≥0} ∞ k=1 be a sequence of two parameter Ornstein Uhlenbeck processes (OUP 2) with coefficients α k>0,β k>0 . A Fernique type inequality is established and the sufficient condition for a.s. l 2 continuity of Y(·) is studied by means of the inequality.

A NOTE ON SAMPLE PATH PROPERTIES OF l^p-VALUED GAUSSIAN PROCESSES

The a.s. sample path properties for l p valued Gaussian processes with stationary increments under some more general conditions are established.

Implementation of Control Algorithms in Small Embedded Systems

This work describes how a control algorithm can be implemented in a small (8-bit) microcontroller for the main purpose of merging embedded systems and control theory in electrical engineering undergraduate classes. Two different methods for discretizing the control expression are compared: Euler transformation and bilinear transformation. The sampling rate’s impact on the algorithm is discussed and theoretical results are verified by an application to a temperature control system in a heating plant. Four control algorithms are compared: PID and PI algorithms discretized with Euler and bilinear transformation, respectively. It is shown that for the heating plant used in this work, a bilinear PI algorithm implemented in a small 8-bit microcontroller outperforms a commercial controller from Panasonic. It is also demonstrated that all the derived algorithms can be implemented using integer calculations only, obviating the need for expensive and time-consuming floating-point calculations. This work bridges the gap between control theory equations and the implementation of control systems in small embedded systems with no inherent floating-point processing power.

Maxima and sum for discrete and continuous time Gaussian processes

We study the asymptotic relation among the maximum of continuous weakly and strongly dependent stationary Gaussian process, the maximum of this process sampled at discrete time points, and the partial sum of this process. It is shown that these two extreme values and the sum are asymptotically independent if the grid of the discrete time points is sufficiently sparse and the Gaussian process is weakly dependent, and asymptotically dependent if the grid points are Pickands grids or dense grids.

GIRSANOV'S THEOREM ON ABSTRACT WIENER SPACES

The moments and absolute continuity of measure valued branching Brownian motions with bounded interacting intensity are investigated. An estimate of higher order moments is obtained.The absolute continuity is verified in the one dimension case. This thereby verifies the conjecture of Méléard and Roelly in .