Conditional Expectation on Inflection Quant Labhttps://inflection-quant.pages.dev/tags/conditional-expectation/Recent content in Conditional Expectation on Inflection Quant LabHugoen-usThu, 28 May 2026 00:00:00 +0000The Brownian Bridge: What Brownian Motion Looks Like When You Know the Endpointshttps://inflection-quant.pages.dev/articles/quant-foundations/brownian_bridge/Thu, 28 May 2026 00:00:00 +0000https://inflection-quant.pages.dev/articles/quant-foundations/brownian_bridge/<h2 id="why-this-matters">Why This Matters</h2> <p>In my earlier article on <a href="../../articles/quant-foundations/understanding_brownian_motion/">Brownian motion</a>, I worked through the forward view: a process starting at a known value, diffusing into an uncertain future. Sometimes we know more than just the starting point. We also know where the process ended up, and we want to characterise the path in between. The object that answers this is the Brownian bridge: a Brownian motion conditioned on its terminal value.</p>