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Path Integrals and the Distribution of Random Paths - Stochastic Processes and PDEs (8/8)

Path integrals provide a way to think about stochastic processes at the level of entire random trajectories rather than probability densities at fixed times. In this video, we derive the path integral for Brownian motion, discuss its interpretation, and apply path-level reasoning to the first passage time problem.

Full Series:
https://www.youtube.com/playlist?list=PLdMM2W7mxqIYZ99-Lj5fV_Nl19bpTn8fk

Timestamps:
00:00 Motivation: Why PDEs Are Not Enough
04:00 Stochastic Simulation and Random Paths
07:20 Derivation of the Path Integral
20:15 First Passage Time and the Reflection Principle

Topics

• Stochastic Processes
• Brownian Motion
• Path Integrals
• Wiener Measure
• Stochastic Differential Equations
• Monte Carlo Simulation
• Action Functional
• First Passage Time
• Reflection Principle
• Lévy Distribution
• Mathematical Finance
• Applied Mathematics

Видео Path Integrals and the Distribution of Random Paths - Stochastic Processes and PDEs (8/8) канала Jingyuan Hu
path integral path integrals stochastic processes brownian motion wiener process wiener measure fokker planck equation applied probability mathematical finance quantitative finance monte carlo simulation stochastic simulation diffusion process first passage time reflection principle levy distribution action functional feynman path integral statistical physics mathematical physics measure theory
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29 мая 2026 г. 8:15:53
00:30:34
Jingyuan Hu
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