# StochasticProcess_psets

**Repository Path**: jackfgao/StochasticProcess_psets

## Basic Information

- **Project Name**: StochasticProcess_psets
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: Not specified
- **Default Branch**: main
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2025-09-26
- **Last Updated**: 2025-09-26

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# StochasticProcess_psets

This repository contains the materials covered in MATH5311 class at University of Texas at Arlington. The textbook used for the class is Stochastic Calculus by Ross. 
Below I summarize each files:
1) HW1: This HW mainly covers Poisson processes. I assume that some theorems regarding Poisson processes such as "conditional expectation of arrival time for i-th shock $S_i$ given n number of events occur by time t (i.e., $N(t)=n$) is uniformly iid" are familiar to the readers. 
2) HW2: This HW mainly Covers discrete time markov chain, its stationary distributions, and state recurrence.
3) HW3: This homework covers continuous time Markov Process particularly birth-death process. Problems involve finding stationary distributions and obtaining exact or approximation.
4) HW4: This homework covers the property of Brownian motions and stochastic differential equations. Ito lemma, Ito isometry, and Feynman-Kac formula are assumed as prior knowledge, and final problem solves the Black-Scholes equation.
5) Final Project: This file contains answers to several SDE. It also covers Fokker-Planck equations to find the evolution of density for some certain SDEs. It also covers numerical solution techniques for parabolic PDEs using Feynman-Kac formula. Implementation is done in Python.
6) Stochastic Process by Ross: the textbook covered in the class.