Stochastic Processes with Applications

A broad introduction to stochastic processes, focusing on their application to describe natural phenomena and on numerical simulations rather than on mathematical formalism.  Define and classify stochastic processes (discrete/continuous time and space, Markov property, and forward and backward dynamics). Explore common stochastic processes (Markov chains, Master equations, Langevin equations) and their key applications in physics, biology, and neuroscience. Use mathematical techniques to analyze stochastic processes and simulate discrete and continuous stochastic processes using Python.

Prerequisites or Prior Knowledge

Calculus, Fourier transforms, probability theory, scientific programming in Python.