The standard diffusion equation assumes a finite mean waiting time and a finite jump variance. When either assumption fails, as it does for tracer particles in turbulent plasmas with long trapping events and large radial jumps, the central limit theorem no longer applies and the diffusion equation is replaced by a fractional diffusion equation derived from a heavy-tailed continuous-time random walk.

Quantum amplitude estimation promises a quadratic speedup over classical Monte Carlo for pricing financial derivatives, but that query-complexity result excludes variance reduction and oracle implementation costs. Testing European and arithmetic Asian calls, the control variate changes the classical baseline sharply while even small path-dependent quantum oracles become deep.

Conventional linear correlation methods do not fully characterize turbulent plasma interactions because they assume Gaussian statistics and do not provide a directional measure of coupling. This report implements nonlinear cross-correlation and transfer entropy on synthetic coupled systems and SWIP HL-2A shot #36656, finding directional asymmetry that is nonuniform across channels and changes in time.

Notes from 'Monte Carlo Methods in Financial Engineering' by Paul Glasserman. These Notes are subject to be constantly updated as I read through more of the textbook.

We explore transition matrices by making a simple Lorem Ipsum generator that accepts any root text. This a test article and is subject to be updated to test the implementation of new features on this blog. This article is incomplete in its explanation.

In this post, we’ll dive into modeling a multi-body system with straightforward numerical methods and a few simplifying assumptions. Focusing on Jupiter and its Galilean moons, we will explore how to use the Runge-Kutta 4th order method. This a test article and is subject to be updated to test the implementation of new features on this blog. This article is incomplete in its explanation.

This is an article I wrote for my Stat Mech 2 course. It's not wholly accurate. This a test article and is subject to be updated to test the implementation of new features on this blog. This article is incomplete in its explanation.