Sefish Mining Fallacy Part 4 - Stochastic Modelling

Definition:

"Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. Distributions of potential outcomes are derived from a large number of simulations (stochastic projections) which reflect the random variation in the input(s). Its application initially started in physics. It is now being applied in engineering, life sciences, social sciences, and finance.

https://en.wikipedia.org/wiki/Stochastic_modelling_(insurance)

Useful probability distributions to understand selfish-mining paper

1. Poisson Distribution: is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.

https://en.wikipedia.org/wiki/Poisson_distribution

https://onlinecourses.science.psu.edu/stat414/node/54

2. Gamma Distribution: is a two-parameter family of continuous probability distributions. The common exponential distribution and chi-squared distribution are special cases of the gamma distribution.

https://en.wikipedia.org/wiki/Gamma_distribution

https://onlinecourses.science.psu.edu/stat414/node/143

For Debate understanding regarding Martingale

Martingales

Stochastic processes deal with the dynamics of probability theory. The concept of stochastic processes enlarges the random variable concept to include time. [1]

[1]Markov Processes for Stochastic Modeling
https://books.google.com/books?isbn=0124078397
Oliver Ibe - 2013 - ‎Mathematics

A martingale captures the essence of a fair game in the sense that regardless of a player’s current and past fortunes, his expected fortune at any time in the future is the same as his current fortune. Thus, on the average, he neither wins nor loses any money. Also, martingales fundamentally deal with conditional expectation. we can consider a martingale as a process whose expected value, conditional on some potential information, is equal to the value revealed by the last available information. Similarly, a submartingale represents a favorable game because the expected fortune increases in the future, while a supermartingale represents an unfavorable game because the expected fortune decreases in the future.

Martingales occur in many stochastic processes. They have also become an important tool in modern financial mathematics because martingales provide one idea of fair value in financial markets. [2]

[2] Markov Processes for Stochastic Modeling, 2nd Edition by Oliver Ibe