19th Ave New York, NY 95822, USA

# 数学代写| 随机过程代考|The Wiener process

A population starts with one individual at time $n=0: Z_{0}=1$.

After one unit of time (at time $n=1$ ) the sole individual produces $Z_{1}$ identical clones of itself and dies. $Z_{1}$ is an $\mathbb{N}_{0}$-valued random variable.

(a) If $Z_{1}$ happens to be equal to 0 the population is dead and nothing happens at any future time $n \geq 2$.

(b) If $Z_{1}>0$, a unit of time later, each of $Z_{1}$ individuals gives birth to a random number of children and dies. The first one has $Z_{1,1}$ children, the second one $Z_{1,2}$ children, etc. The last, $Z_{1}^{\text {th }}$ one, gives birth to $Z_{1, Z_{1}}$ children. We assume that the distribution of the number of children is the same for each individual in every generation and independent of either the number of individuals in the generation and of the number of children the others have. This distribution, shared by all $Z_{n, i}$ and $Z_{1}$, is called the offspring distribution. The total number of individuals in the second generation is now
$$Z_{2}=\sum_{k=1}^{Z_{1}} Z_{1, k}$$
(c) The third, fourth, etc. generations are produced in the same way. If it ever happens that $Z_{n}=0$, for some $n$, then $Z_{m}=0$ for all $m \geq n$ – the population is extinct. Otherwise,
$$Z_{n+1}=\sum_{k=1}^{Z_{n}} Z_{n, k}$$

my-assignmentexpert™ 随机过程Stochastic Process作业代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。my-assignmentexpert™， 最高质量的随机过程Stochastic Process作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此随机过程Stochastic Process作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

my-assignmentexpert™ 为您的留学生涯保驾护航 在统计Statistics作业代写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。我们的专家在随机过程Stochastic Process代写方面经验极为丰富，各种随机过程Stochastic Process相关的作业也就用不着 说。

• 时间序列分析Time-Series Analysis
• 马尔科夫过程 Markov process
• 随机最优控制stochastic optimal control
• 粒子滤波 Particle Filter
• 采样理论 sampling theory

## 数学代写| 随机过程代考|basic properties

Most of the random processes considered so far are ‘discrete’ in the sense that they take values in the integers or in some other countable set. Perhaps the simplest example is simple random walk $\left{S_{n}\right}$, a process which jumps one unit to the left or to the right at each step. This random walk $\left{S_{n}\right}$ has two interesting and basic properties:
(a) time-homogeneity, in that, for all non-negative $m$ and $n, S_{m}$ and $S_{m+n}-S_{n}$ have the same distribution (we assume $S_{0}=0$ ); and
(b) independent increments, in that the increments $S_{n_{l}}-S_{m_{l}}(i \geq 1)$ are independent whenever the intervals $\left(m_{i}, n_{i}\right]$ are disjoint.

## 数学代写| 随机过程代考|random variables

The vector of random variables $W\left(t_{1}\right), W\left(t_{1}\right), \ldots, W\left(t_{n}\right)$ has the multivariate normal distribution with zero means and covariance matrix $\left(v_{i j}\right)$ where $v_{i j}=\sigma^{2} \min \left{t_{i}, t_{j}\right}$.
Proof. By assumption, $W\left(t_{i}\right)$ has the normal distribution with zero mean and variance $\sigma^{2} t_{i}$. It therefore suffices to prove that $\operatorname{cov}(W(s), W(t))=\sigma^{2} \min {s, t}$. Now, if $s<t$, then
$$\mathbb{E}(W(s) W(t))=\mathbb{E}\left(W(s)^{2}+W(s)[W(t)-W(s)]\right)=\mathbb{E}\left(W(s)^{2}\right)+0$$
since $W$ has independent increments and $\mathbb{E}(W(s))=0$. Hence
$$\operatorname{cov}(W(s), W(t))=\operatorname{var}(W(s))=\sigma^{2} s$$

## 数学代写| 随机过程代考|BASIC PROPERTIES

b独立增量，因为增量小号n一世−小号米一世(一世≥1)每当间隔是独立的(米一世,n一世]是不相交的。

## 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。