## Markov Chain an Introduction (2014)

A Markov chain, named after Andrey Markov is a mathematical system that experiences transitions from one state to another, between a finite or countable number of possible states. Markov chain is a random process usually characterized as memoryless: the next state depends only on the …

## Random Walk Probability of Returning to Origin after n steps

Random Walk Probability of Returning to Origin Assume that the walk starts at $x=0$ with steps to the right or left occurring with probabilities $p$ and $q=1-p$. We can write the position $X_n$ after $n$ steps as$X_n=R_n-L_n \tag{1}$where $R_n$ is the number of right or …

## Simple Random Walk (Unrestricted Random Walk)

A simple random walk (or unrestricted random walk) on a line or in one dimension occurs with probability $p$ when the walker steps forward (+1) and/or has probability $q=1-p$ if the walker steps back ($-1$). For ith step, the modified Bernoulli random variable $W_i$ (takes …

## Random Walks Model: A Mathematical Formalization of Path

A random walk (first introduced by Karl Pearson in 1905) is a mathematical formalization of a path consisting of a series of random steps. Random Walks Example The following are some example related to random walks Suppose there are $a+1$ positions marked out on a …