Probability and Stochastic Processes: Work Examples
暫譯: 機率與隨機過程:實作範例

Odile Pons

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商品描述

The book is intended to undergraduate students, it presents exercices and problems with rigorous solutions covering the mains subject of the course with both theory and applications.The questions are solved using simple mathematical methods: Laplace and Fourier transforms provide direct proofs of the main convergence results for sequences of random variables.The book studies a large range of distribution functions for random variables and processes: Bernoulli, multinomial, exponential, Gamma, Beta, Dirichlet, Poisson, Gaussian, Chi2, ordered variables, survival distributions and processes, Markov chains and processes, Brownian motion and bridge, diffusions, spatial processes.

商品描述(中文翻譯)

本書旨在為大學本科生而設,提供了涵蓋課程主要主題的練習題和問題,並附有嚴謹的解答,包含理論與應用。這些問題使用簡單的數學方法進行解決:拉普拉斯變換(Laplace transforms)和傅立葉變換(Fourier transforms)提供了隨機變數序列主要收斂結果的直接證明。本書研究了隨機變數和過程的各種分佈函數:伯努利(Bernoulli)、多項式(multinomial)、指數(exponential)、伽瑪(Gamma)、貝塔(Beta)、狄利克雷(Dirichlet)、泊松(Poisson)、高斯(Gaussian)、卡方(Chi2)、有序變數、生存分佈和過程、馬可夫鏈(Markov chains)和過程、布朗運動(Brownian motion)及橋接(bridge)、擴散(diffusions)、空間過程。