Torbjörn Thedéen

Convergence and invariance questions for point systems inR 1 under random motion

In section 2 we introduce and study the independence property for a sequence of two-dimensional random variables and by means of this property we define independent motion in section 3. Section 4 is mainly a survey of known results about the convergence of the spatial distribution of the point system as the timet→∞. In theorem 5.1 we show that the only distributions which are time-invariant under given reversible motion of non-degenerated type are the weighted Poisson ones. Lastly in section 6 we study a more general type of random motion where the position of a point after translation is a functionf of its original position and its motion ability. We consider functionsf which are monotone in the starting position. Limiting ourselves to the case when the point system initially is weighted Poisson distributed with independent motion abilities, we prove in theorem 6.1 that this is the case also after the translations, if and only if the functionf is linear in the starting position. In the paper also some implications of our results to the theory of road traffic with free overtaking are given.

Vulnerability of Infrastructures

Society depends on the functioning of working connections for the transportation of individuals and goods, mail and telephony, etc. The fast technical development has changed these systems into larger and automated ones. The number of individual journeys as well as their lengths has increased and this holds also for telecommunications. The average journey length in the European Union in 2004 was 12 000 km per capita and it has increased by 2% annually during the last 10 years. Internal and external trade has increased dramatically, and this in turn has led to more transportation of persons and goods.

Reflections on Risks and Technology

Human activities are connected with risks. Throughout our history, managing and controlling these risks has built on the experience of generations. Industrialization meant a partly new situation. People began to work increasingly in groups, in mines and in factories. New technology was introduced, although slowly at first and in small establishments. Experience was lacking, and the technology was often difficult to understand. An accident could hit many people at the same time. In order to handle the risks, one tried to combine the few available data on accidents with engineering calculations – the start of what would become modern risk analysis.

On stochastic stationarity of renewal processes

We shall consider point systems inR1 which are stationary renewal distributed. We let the points undergo random translations which are assumed to be independent identically distributed random variables with a non-degenerate distribution function. The translations are also independent of the starting positions. It is shown in theorem 3.1 that the only distribution of the points which is conserved after the random translations is the Poisson one. Finally in section 4 we give a characterization of renewal processes on the positive semiaxis in terms of conditional mean values.

Introduction: the Global Risk Arena, Technological Systems and This Book

The global citizen of the twenty-first century faces a wide spectrum of risks, such as from transportation, ionizing radiation, the propagation of contagious diseases, terrorism, natural disasters, and global climate change. Some of them, for instance the risk of a motorcycle accident, affect only individuals and have merely occasional direct impacts on society. Nevertheless the accumulation of these individual risks is leading to major long-term changes in risk patterns.

Risks in the Conversion of Energy

Modern society is dependent upon the availability of an abundant supply of cheap energy. The use of energy is basically a positive factor necessary for our prosperity, but like all other industrial activities, the production of energy can have negative effects on human beings and on the environment. Today, energy is obtained and converted to a great extent in large systems. The chemical energy stored in fossil fuels is, for example, converted by combustion into heat energy, which can be used directly for heating purposes. The heat can also be converted into kinetic energy via steam in turbines and via generators into electricity. When this is subsequently delivered to the consumer, some of the electrical energy is lost.

How dangerous is it to travel

In this chapter, we shall mainly consider risks to persons and only briefly consider risks to the environment (compare with Chapter 6). Risks connected with traffic by road, by rail, in the air, and at sea are considered. The economic progress of society is accompanied by an increase in transportation, which has not been replaced by telecommunication. On the contrary, telecommunication has given rise to more travel. The travel mode distribution has changed from a dominant role of travel by sea, horse, and on foot to include car, rail, and air traffic. The transportation of individuals has increased dramatically in the Western world. In the European Union (EU), for example, the daily travel distance per person has increased by 20 % during the last decade and was, at the beginning of the twenty-first century, 36 kilometers per day (EU, 2007). The modal split of the traffic load in EU is given in Table 9.1.