Author(s)

Xiaofeng Xu

Corresponding Author

Xiaofeng Xu

ABSTRACT

Stochastic processes are regarded as a dynamic component of probability theory. By understanding the theory of stochastic processes, people can investigate random phenomena under a given time basis. Random phenomenon concept and investigation is vital in the development of mathematical models. Generally, stochastic processes represent a group of random variables that have been indexed against another variable or set of factors. Poisson phenomena, for instance, the radioactive decay, Markov processes, and time series, with the indexing parameter relating to time, are some of the most fundamental forms of stochastic processes. The type of changes in the variables concerning time is the focus of this indexing, which might be continuous or discrete. The random walk phenomena are an example of a Markov chain process I will be researching in this paper. Although the terminology is most commonly used to refer to a subcategory of Markov chains, several time-dependent phenomena are referred to as random walks, with a prefix emphasizing their unique qualities. Random walks may be used to represent a variety of phenomena in humans and animals, such as diffusion, interactions, and attitudes, as well as to extract information about key entities or dense clusters of entities in a network. For decades, random walks have been investigated on regular lattices and networks with various architectures. This research paper shifts the focus to multiple types of random walks, processes, and their applications in statistics and real life.

KEYWORDS

Random Walk, Stochastic Processes, Markov chain, Self-Avoiding Walk, Spacey Random Walks, Bernoulli Excursion, Gaussian Random Walks