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Hacker News<p>An Introduction to Stochastic Calculus</p><p><a href="https://bjlkeng.io/posts/an-introduction-to-stochastic-calculus/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">bjlkeng.io/posts/an-introducti</span><span class="invisible">on-to-stochastic-calculus/</span></a></p><p><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>HackerNews</span></a> <a href="https://mastodon.social/tags/StochasticCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>StochasticCalculus</span></a> <a href="https://mastodon.social/tags/Introduction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Introduction</span></a> <a href="https://mastodon.social/tags/MathFinance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MathFinance</span></a> <a href="https://mastodon.social/tags/ProbabilityTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ProbabilityTheory</span></a> <a href="https://mastodon.social/tags/Education" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Education</span></a></p>
Fabio Capela<p>Geometric Brownian Motion is the stochastic differential equation used to model stock prices: dS = μSdt + σSdW. This forms the mathematical foundation for options pricing, Monte Carlo market simulations, and much of modern finance theory. Fascinating intersection of math and markets! <a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> <a href="https://mathstodon.xyz/tags/FinancialModeling" class="mention hashtag" rel="tag">#<span>FinancialModeling</span></a> <a href="https://mathstodon.xyz/tags/RandomWalk" class="mention hashtag" rel="tag">#<span>RandomWalk</span></a></p>
Hacker News<p>Introduction to Stochastic Calculus — <a href="https://jiha-kim.github.io/posts/introduction-to-stochastic-calculus/" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">jiha-kim.github.io/posts/intro</span><span class="invisible">duction-to-stochastic-calculus/</span></a><br><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>HackerNews</span></a> <a href="https://mastodon.social/tags/Introduction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Introduction</span></a> <a href="https://mastodon.social/tags/to" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>to</span></a> <a href="https://mastodon.social/tags/Stochastic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Stochastic</span></a> <a href="https://mastodon.social/tags/Calculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Calculus</span></a> <a href="https://mastodon.social/tags/StochasticCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>StochasticCalculus</span></a> <a href="https://mastodon.social/tags/MathFinance" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>MathFinance</span></a> <a href="https://mastodon.social/tags/DataScience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>DataScience</span></a> <a href="https://mastodon.social/tags/Learning" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Learning</span></a></p>
ZerusMaximus<p>I was searching for some study material, and found that most of <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="tag">#<span>mathematics</span></a> textbooks, at least of a more advanced level, are incredibly dense in notation. It makes sense in a way, but similarly, where appropriate, a visual, even geometric intuition, can sometimes shed light on difficult topics. <br />I&#39;m thinking mostly of Tristan Needham&#39;s &quot;Visual Differential Geometry and Forms&quot;, as far as visual illustration of concepts, ideas, or &quot;Visual Complex Analysis&quot;. Are there any similarly rich books covering topics such as <a href="https://mathstodon.xyz/tags/tensoralgebra" class="mention hashtag" rel="tag">#<span>tensoralgebra</span></a>, <a href="https://mathstodon.xyz/tags/statistics" class="mention hashtag" rel="tag">#<span>statistics</span></a>, <a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="tag">#<span>probability</span></a>, <a href="https://mathstodon.xyz/tags/stochasticcalculus" class="mention hashtag" rel="tag">#<span>stochasticcalculus</span></a>?</p>
Francis Ho<p>Here is a concrete visualization/example of a filtration for a stochastic process. Using the spreadsheet "filter" function makes it clear why we call it a filtration, because we are filtering out the outcomes that are no longer possible.</p><p><a href="https://docs.google.com/spreadsheets/d/1UwKdcoTnfMDEeWOClWN9zuSwCDKrcmM7pVBlMvx0vgI/edit?usp=sharing" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">docs.google.com/spreadsheets/d</span><span class="invisible">/1UwKdcoTnfMDEeWOClWN9zuSwCDKrcmM7pVBlMvx0vgI/edit?usp=sharing</span></a></p><p><a href="https://hachyderm.io/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>probability</span></a> <a href="https://hachyderm.io/tags/stochasticcalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>stochasticcalculus</span></a></p>
Francis Ho<p>My distance and number of steps for a walk are approximations of the variation over the interval of my location, AKA total variation. </p><p><a href="https://en.wikipedia.org/wiki/Total_variation" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">en.wikipedia.org/wiki/Total_va</span><span class="invisible">riation</span></a></p><p>They are finite because even though you may think it is so, I am not really doing a random walk (which would have infinite variation and finite quadratic variation). 😎</p><p><a href="https://hachyderm.io/tags/BrownianMotion" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>BrownianMotion</span></a> <a href="https://hachyderm.io/tags/stochasticCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>stochasticCalculus</span></a></p>
Almost Sure<p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> notes: Cadlag Modifications</p><p><a href="https://almostsuremath.com/2009/12/18/cadlag-modifications/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2009/12/18/</span><span class="invisible">cadlag-modifications/</span></a></p>
Almost Sure<p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> notes: Upcrossings, Downcrossings, and Martingale Convergence.</p><p><a href="https://almostsuremath.com/2009/12/06/upcrossings-downcrossings-and-martingale-convergence/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2009/12/06/</span><span class="invisible">upcrossings-downcrossings-and-martingale-convergence/</span></a></p>
Almost Sure<p>New almostsure blog post: Model-Independent discrete barrier adjustments.</p><p>When monitoring a continuous barrier, but sample discretely, adjustments are required for good convergence.<br />This looks at how it can be done in a generic way</p><p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a></p><p><a href="https://almostsuremath.com/2023/07/09/model-independent-discrete-barrier-adjustments/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2023/07/09/</span><span class="invisible">model-independent-discrete-barrier-adjustments/</span></a></p>
Almost Sure<p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> notes: Martingales and Elementary Integrals</p><p><a href="https://almostsuremath.com/2009/12/06/martingales-and-elementary-integrals/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2009/12/06/</span><span class="invisible">martingales-and-elementary-integrals/</span></a></p>
Almost Sure<p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> notes: Predictable Stopping Times</p><p><a href="https://almostsuremath.com/2009/11/30/predictable-stopping-times/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2009/11/30/</span><span class="invisible">predictable-stopping-times/</span></a></p>
Almost Sure<p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> notes: Sigma Algebras at a Stopping Time</p><p><a href="https://almostsuremath.com/2009/11/23/sigma-algebras-at-a-stopping-time/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2009/11/23/</span><span class="invisible">sigma-algebras-at-a-stopping-time/</span></a></p>
Almost Sure<p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> notes: Stopping Times and the Debut Theorem</p><p><a href="https://almostsuremath.com/2009/11/15/stopping-times-and-the-debut-theorem/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2009/11/15/</span><span class="invisible">stopping-times-and-the-debut-theorem/</span></a></p>
Almost Sure<p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> notes: Filtrations and adapted processes</p><p><a href="https://almostsuremath.com/2009/11/08/filtrations-and-adapted-processes/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2009/11/08/</span><span class="invisible">filtrations-and-adapted-processes/</span></a></p>
Almost Sure<p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> notes: Stochastic Processes, Indistinguishability and Modifications</p><p>Where it all began – the very first post of my notes.</p><p><a href="https://almostsuremath.com/2009/11/03/stochastic-processes-indistinguishability-and-modifications/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2009/11/03/</span><span class="invisible">stochastic-processes-indistinguishability-and-modifications/</span></a></p>
Almost Sure<p>Follow me here on mastodon for posts on maths, physics, and especially <a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a> and <a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="tag">#<span>probability</span></a> related material.</p><p>Also, check out my blog “Almost Sure”</p><p><a href="https://almostsuremath.com" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">almostsuremath.com</span><span class="invisible"></span></a></p><p>I may or may not be posting on twitter (we’ll see how that goes…), but will cross-post any original content here.</p>
Almost Sure<p>New almostsure blog post!</p><p>This looks at how you can adjust the values of a discretely sampled process in order to accurately monitor a continuous barrier condition.</p><p><a href="https://mathstodon.xyz/tags/StochasticCalculus" class="mention hashtag" rel="tag">#<span>StochasticCalculus</span></a></p><p><a href="https://almostsuremath.com/2023/07/01/discrete-barrier-approximations/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">almostsuremath.com/2023/07/01/</span><span class="invisible">discrete-barrier-approximations/</span></a></p>
ELLIS<p>We look forward to new exciting collaborations &amp; papers emerging from our ELLIS/ELISE program workshop ending in Tübingen, Germany, today - an intense exchange on <a href="https://ellis.social/tags/StochasticCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>StochasticCalculus</span></a>, <a href="https://ellis.social/tags/StatisticalPhysics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>StatisticalPhysics</span></a> &amp; <a href="https://ellis.social/tags/ML" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ML</span></a> with passionate European scientists that we plan to repeat next year! </p><p>Workshop overview: <a href="https://sites.google.com/view/scspo23/home" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="ellipsis">sites.google.com/view/scspo23/</span><span class="invisible">home</span></a></p>