Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation

The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large classes of functional random variables, it is well known as the invariance principle for LIL which provide an extremely powerful tool in probability and statistical inference. But recently many phenomena show that the linearity of probability is a limit for applications, for example in finance, statistics. As while a nonlinear expectation--- G-expectation has attracted extensive attentions of mathematicians and economists, more and more people began to study the nature of the G-expectation space. A natural question is: Can the classical invariance principle for LIL be generalized under G-expectation space? This paper gives a positive answer. We present the invariance principle of G-Brownian motion for the law of the iterated logarithm under G-expectation

Switching cells and their implications for power electronic circuits

Journal ArticleThis paper will introduce two basic switching cells, P-cell and N-cell, along with their implications and applications in power electronic circuits. The concept of switching cells in power electronic circuits started in the late 1970's. The basic cells presented in this paper have one switching element (transistor) and one diode. The P-cell is the mirror circuit of the N-cell and vice-versa, and this paper suggests that (1) most power electronic circuits can be analyzed and re-constructed using these basic switching cells, (2) single, dual, and 6-pack switching modules should be configured and laid-out according to the basic switching cells and not necessarily the conventional way used by industry, and (3) many benefits such as minimal parasitic inductance and dead-time elimination or minimization may come about. The present paper will describe the construction and operation of these basic switching cells, and it will also show a sequential method to reconstruct several classical dc-dc converters, a voltage source inverter (VSI), and a current source inverter (CSI) using these basic switching cells. In addition, the use of basic switching cells introduces some new topologies of dc-dc converters that originate from the buck, boost, and Cuk converter for negative input voltages. This paper will also illustrate the experimental results of the new and existing topologies constructed from basic switching cells