### 统计代写|随机过程作业代写stochastic process代考|Notion of Stochastic Processes

statistics-lab™ 为您的留学生涯保驾护航 在代写 随机过程stochastic process方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写随机过程stochastic process方面经验极为丰富，各种代写 随机过程stochastic process相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|随机过程作业代写stochastic process代考|Notion of Stochastic Processes

Loosely speaking, the mathematical description of a random phenomenon as it changes in time is a stochastic process. Since the last century there has been greater realisation that stochastic (or non-deterministic) models are more realistic than deterministic models in many situations. Observations taken at different time points rather than those taken at a fixed period of time began to draw the attention of scientists. The physicists and communication engineers played a leading role in the development of dynamic indeterminism. Many a phenomenon occurring in physical and life sciences are studied not only as a random phenomenon but also as one changing with time or space. Similar considerations are also made in other areas such as social sciences, economics and management sciences, and so on. The scope of applications of stochastic processes which are functions of time or space or both is ever increasing.

A stochastic process is a family of random variables $\left{X_{t}\right}$, where $t$ takes values in the index set $T$ (sometimes called a parameter set or a time set).
The values of $X$, are called the state space and will be denoted by $S$.
If $T$ is countable then the stochastic process is called a stochastic sequence (or discrete parameter stochastic process). If $S$ is countable then the stochastic process is called a discrete state (space) process.

If $S$ is a subset of the real line the stochastic process is called a real valued process.
If $T$ takes continuously uncountable number of values like $(0, \infty)$ or $(-\infty, \infty)$ the stochastic process is called a continuous time process. To emphasize its dependence on $t$ and sample point $w$, we shall denote the stochastic process by $X(t, w), t \in T, w \in \Omega$ i.e. for each $w \in \Omega, X_{t}=X(t$,
$w)$ is a function of $t$.
This graph is known as the “typical sample function” or “realization of the stochastic process” $X(t, w)$.

## 统计代写|随机过程作业代写stochastic process代考|Different Types of Stochastic Processes

Following are the most important types of stochastic processes we come across:

1. Independent stochastic sequence (Discrete time process)
$T={1,2,3, \ldots}$ and $\left{X_{t}, t \in T\right}$ are independent random variables.
2. Renewal process (Discrete time process)
Here $T={0,1,2,3, \ldots], S=[0, \infty]$.
If $X_{n}$ are i.i.d. non-negative random variables and $S_{n}=X_{1}+\ldots+X_{n}$ then $\left{S_{n}\right}$ forms a discrete time (renewal process).
3. Independent increment process (Continuous time process)
$T=\left{t_{0}, \infty\right}$, where $t_{0}$ be any real number (+or $-$ ). For every
$$t_{0}<t_{1}<\ldots<t_{n}, t_{i} \in T, i=1,2, \ldots, n$$
if $X_{t_{0}}, X_{t_{1}}-X_{t_{0}}, X_{t_{2}}-X_{t_{1}}, \ldots, X_{t_{n}}-X_{t_{n-1}}$ are independent for all possible choices of $(1.1)$, then the stochastic process $\left{X_{1}, t \in T\right}$ is called independent increment stochastic process.
4. Markov process
If $P\left[X_{l_{n+1}} \in A \mid X_{l_{n}}=a_{n}, X_{t_{n-1}}=a_{n-1}, \ldots, X_{t_{0}}=a_{0}\right]$ $=P\left[X_{t_{n+1}} \in A \mid X_{t_{n}}=a_{n}\right]$ holds for all choices of
$$t_{0}<t_{1}<t_{2}<\ldots<t_{n+1}, t_{i} \in T \cdot i=0,1,2, \ldots, n+1$$
and $A \in . D$, the Borel field of the state space $S$, then $\left{X_{t}, t \in T\right}$ is called a Markov process.
5. Martingale or fair game process
If $\quad E\left[X_{t_{n+1}} \mid X_{t_{n}}=a_{n}, X_{t_{n-1}}=a_{n-1}, \ldots, X_{t_{0}}=a_{0}\right]=a_{n}$
i.e. $E\left[X_{t_{n+1}} \mid X_{t_{n}}, \ldots, X_{t_{0}}\right]=X_{t_{n}}$ a.s. for all choices of the partition (1.1), then $\left{X_{t}, t \in T\right}$ is called a Martingale process.
6. Stationary process
If the joint distribution of $\left(X_{t_{1}+t_{h}}, \ldots, X_{t_{n}+h}\right)$ are the same for all $h>0$ and
$$t_{1}<t_{2}<\ldots<t_{n}, t_{i} \in T, t_{i}+h \in T$$
then $\left{X_{t}, t \in T\right}$ is called a stationary process (strictly stationary process).

## 统计代写|随机过程作业代写stochastic process代考|Examples of stationary processes

(a) Electrical pulses in communication theory are often postulated to describe a stationary process. Of course, in any physical system there is a transient period at the beginning of a signal. Since typically this has a short duration compared to the signal length, a stationary model may be appropriate. In electrical communication theory, often both the electrical potential and the current are represented as complex variables. Here we may encounter complex-valued stationary processes.
(b) The spatial and/or planar distributions of stars of galaxies, plants and animals, are often stationary. Time parameter set $T$ might be Euclidean space, the surface of a sphere or the plane.

A stationary distribution may be postulated for the height of a wave and $T$ is taken to be a set of longitudes and latitudes, again two dimensional.
(c) Economic time series, such as unemployment, gross national product, national income etc., are often assumed to correspond to a stationary process, at least after some correction for long-term growth has been made.

## 统计代写|随机过程作业代写stochastic process代考|Different Types of Stochastic Processes

1. 独立随机序列（离散时间过程）
吨=1,2,3,…和\left{X_{t}, t \in T\right}\left{X_{t}, t \in T\right}是独立的随机变量。
2. 更新过程（离散时间过程）
这里 $T={0,1,2,3, \ldots], S=[0, \infty].一世FX_{n}一种r和一世.一世.d.n这n−n和G一种吨一世在和r一种nd这米在一种r一世一种bl和s一种ndS_{n}=X_{1}+\ldots+X_{n}吨H和n\left{S_{n}\right}$ 形成一个离散时间（更新过程）。
3. 独立增量过程（Continuous time process）
T=\left{t_{0}, \infty\right}T=\left{t_{0}, \infty\right}， 在哪里吨0是任何实数（+或−）。对于每一个
吨0<吨1<…<吨n,吨一世∈吨,一世=1,2,…,n
如果X吨0,X吨1−X吨0,X吨2−X吨1,…,X吨n−X吨n−1对于所有可能的选择都是独立的(1.1)，然后是随机过程\left{X_{1}, t \in T\right}\left{X_{1}, t \in T\right}称为独立增量随机过程。
4. 马尔可夫过程
If磷[Xln+1∈一种∣Xln=一种n,X吨n−1=一种n−1,…,X吨0=一种0] =磷[X吨n+1∈一种∣X吨n=一种n]适用于所有选择
吨0<吨1<吨2<…<吨n+1,吨一世∈吨⋅一世=0,1,2,…,n+1
和一种∈.D, 状态空间的 Borel 场小号， 然后\left{X_{t}, t \in T\right}\left{X_{t}, t \in T\right}称为马尔科夫过程。
5. 鞅或公平博弈过程
If和[X吨n+1∣X吨n=一种n,X吨n−1=一种n−1,…,X吨0=一种0]=一种n
IE和[X吨n+1∣X吨n,…,X吨0]=X吨n至于分区（1.1）的所有选择，那么\left{X_{t}, t \in T\right}\left{X_{t}, t \in T\right}称为鞅过程。
6. 平稳过程
如果联合分布(X吨1+吨H,…,X吨n+H)所有人都一样H>0和
吨1<吨2<…<吨n,吨一世∈吨,吨一世+H∈吨
然后\left{X_{t}, t \in T\right}\left{X_{t}, t \in T\right}称为平稳过程（strictly平稳过程）。

## 统计代写|随机过程作业代写stochastic process代考|Examples of stationary processes

(a) 通信理论中的电脉冲通常被假设为描述一个平稳的过程。当然，在任何物理系统中，信号开始时都有一个瞬态周期。由于与信号长度相比，这通常具有较短的持续时间，因此固定模型可能是合适的。在电通信理论中，通常电势和电流都表示为复变量。在这里，我们可能会遇到复值平稳过程。
(b) 星系、植物和动物的恒星的空间和/或平面分布通常是静止的。时间参数集吨可能是欧几里得空间、球面或平面。

(c) 经济时间序列，例如失业、国民生产总值、国民收入等，通常被假定为对应于一个平稳过程，至少在对长期增长进行了一些修正之后。

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。