Building the Compound Poisson Process
نویسنده
چکیده
Abstract. This paper begins by defining the basic aspects of probability, including the probability space and random variables. We explore the types and qualities of random variables, as well as di↵erent distributions and their properties, with the goal of building the Poisson Process, and finally the Compound Poisson Process. This is an important counting process that can be applied to many interesting real life situations.
منابع مشابه
Numerical solution and simulation of random differential equations with Wiener and compound Poisson Processes
Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...
متن کاملCascaded stochastic processes in optics
and key words Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem : how an optical field is converted into a sequence of photoelectrons upon detection . Their choice of problem could not have been better, nor thei r timing more judicious. In a paper entitled "Photoelectron Shot Noise", published in the Journal of Mathematical Physics in 1970, when qua...
متن کاملFuzzy Random Homogeneous Poisson Process and Compound Poisson Process
By dealing with interarrival times as exponentially distributed fuzzy random variables, a fuzzy random homogeneous Poisson process and a fuzzy random compound Poisson process are respectively defined. Several theorems on the two processes are provided, respectively.
متن کاملFractional Poisson Process
For almost two centuries, Poisson process with memoryless property of corresponding exponential distribution served as the simplest, and yet one of the most important stochastic models. On the other hand, there are many processes that exhibit long memory (e.g., network traffic and other complex systems). It would be useful if one could generalize the standard Poisson process to include these p...
متن کاملPoisson processes , ordinary and compound
The Poisson process is a stochastic counting process that arises naturally in a large variety of daily-life situations. We present a few definitions of the Poisson process and discuss several properties as well as relations to some well-known probability distributions. We further briefly discuss the compound Poisson process.
متن کامل