Journal•ISSN: 0021-9002

# Journal of Applied Probability

Cambridge University Press

About: Journal of Applied Probability is an academic journal published by Cambridge University Press. The journal publishes majorly in the area(s): Markov chain & Markov process. It has an ISSN identifier of 0021-9002. Over the lifetime, 5457 publications have been published receiving 135917 citations. The journal is also known as: JAP.

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TL;DR: In this paper, the authors provide a rigorous foundation for the second-order analysis of stationary point processes on general spaces, including the line and hyperplane processes of Davidson and Krickeberg.

Abstract: This paper provides a rigorous foundation for the second-order analysis of stationary point processes on general spaces. It illuminates the results of Bartlett on spatial point processes, and covers the point processes of stochastic geometry, including the line and hyperplane processes of Davidson and Krickeberg. The main tool is the decomposition of moment measures pioneered by Krickeberg and Vere-Jones. Finally some practical aspects of the analysis of point processes are discussed.

1,803 citations

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TL;DR: In this article, a new Markov chain is introduced which can be used to describe the family relationships among n individuals drawn from a particular generation of a large haploid population, and the properties of this process can be studied, simultaneously for all n, by coupling techniques.

Abstract: A new Markov chain is introduced which can be used to describe the family relationships among n individuals drawn from a particular generation of a large haploid population. The properties of this process can be studied, simultaneously for all n, by coupling techniques. Recent results in neutral mutation theory are seen as consequences of the genealogy described by the chain.

1,495 citations

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TL;DR: In this article, the Lagrange multiplier associated with this constraint defines an index which reduces to the Gittins index when projects not being operated are static, and arguments are advanced to support the conjecture that, for m and n large in constant ratio, the policy of operating the m projects of largest current index is nearly optimal.

Abstract: We consider a population of n projects which in general continue to evolve whether in operation or not (although by different rules). It is desired to choose the projects in operation at each instant of time so as to maximise the expected rate of reward, under a constraint upon the expected number of projects in operation. The Lagrange multiplier associated with this constraint defines an index which reduces to the Gittins index when projects not being operated are static. If one is constrained to operate m projects exactly then arguments are advanced to support the conjecture that, for m and n large in constant ratio, the policy of operating the m projects of largest current index is nearly optimal. The index is evaluated for some particular projects.

1,092 citations

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TL;DR: In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development as discussed by the authors.

Abstract: In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.

1,026 citations

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TL;DR: A summary of the various stochastic approaches and applications to chemical reaction kinetics can be found in this paper, but before discussing these we first briefly introduce the basic ideas and definitions of classical or deterministic chemical kinetics.

Abstract: In this article we shall present a summary of the various stochastic approaches and applications to chemical reaction kinetics, but before discussing these we first briefly introduce the basic ideas and definitions of classical or deterministic chemical kinetics. One of the basic questions to which chemists address themselves is the rate of chemical reactions, or in other words, how long it takes for a chemical reaction to attain completion, or equilibrium. Apparently the first significant quantitative investigation was made in 1850 by L. Wilhelmy [93]. He studied the inversion of sucrose (cane sugar) in aqueous solutions of acids, whose reaction is He found empirically that the rate of decrease of concentration of sucrose was simply proportional to the concentration remaining unconverted, i.e., if S(t) is the concentration of sucrose, then The constant of proportionality is called the rate constant of the reaction. If S o is the initial concentration of sucrose, then Since then an enormous number of reactions has been studied and the field of chemical kinetics is now one of the largest areas of chemical research. The importance of the field lies in the fact that it yields concise expressions for the time dependence of reactions, predicts yields, optimum economic conditions, and gives one much insight into the actual molecular processes involved. The detailed molecular picture of a reaction process is called the mechanism of the reaction.

925 citations