https://math.byu.edu/wiki/index.php?action=history&feed=atom&title=Math_637 2026-07-16T04:17:54Z Revision history for this page on the wiki MediaWiki 1.26.3 https://math.byu.edu/wiki/index.php?title=Math_637&diff=3657&oldid=prev 2018-03-29T19:02:03Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 19:02, 29 March 2018</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19" >Line 19:</td> <td colspan="2" class="diff-lineno">Line 19:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=== Prerequisites ===</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=== Prerequisites ===</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>This course has [[Math <del class="diffchange diffchange-inline">543</del>]] as a prerequisite, so it can build on the work done in that class.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>This course has [[Math <ins class="diffchange diffchange-inline">646</ins>]] as a prerequisite, so it can build on the work done in that class.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=== Minimal learning outcomes ===</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>=== Minimal learning outcomes ===</div></td></tr> </table>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_637&diff=3656&oldid=prev 2018-03-29T19:01:29Z

<p>Created page with &quot;== Catalog Information == === Title === Advanced Probability 2. === Credit Hours === 3 === Prerequisite === <a href="/wiki/index.php/Math_636" class="mw-redirect" title="Math 636">Math 636</a>. === Recommended === <a href="/wiki/index.php/Math_341" class="mw-redirect" title="Math 341">Math 341</a>, [[Math 342|342]...&quot;</p> <p><b>New page</b></p><div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Probability 2.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Prerequisite ===<br /> [[Math 636]].<br /> <br /> === Recommended ===<br /> [[Math 341]], [[Math 342|342]], Stat 441(?); or equivalents.<br /> <br /> === Description ===<br /> Advanced concepts in modern probability. Convergence theorems and laws of large numbers. Stationary processes and ergodic theorems. Martingales. Diffusion processes and stochastic integration.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> This course has [[Math 543]] as a prerequisite, so it can build on the work done in that class.<br /> <br /> === Minimal learning outcomes ===<br /> Outlined below are topics that all successful Math 544 students should understand well. As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> #The Daniell-Kolmogorov Theorem<br /> #Stochastic processes and filtrations<br /> # Continuous-time Martingales<br /> # Brownian motion<br /> # Gaussian processes<br /> # Levy processes<br /> # Regular conditional probabilities<br /> #Markov processes<br /> #Stochastic integration<br /> # Itô's formula&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;<br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> * Achim Klenke, ''Probability Theory: A Comprehensive Course'', Springer, 2008.<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> None</div>

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