Stochastic Processes
http://www.maa.org/taxonomy/term/42058/0
enChutes and Ladders for the Impatient
http://www.maa.org/programs/maa-awards/writing-awards/chutes-and-ladders-for-the-impatient
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span style="font-size: small;"><span style="font-family: verdana,geneva;"><strong>Award:</strong> George PĆ³lya</span></span></p>
<p><span style="font-size: small;"><span style="font-family: verdana,geneva;"><span style="font-size: small;"><strong>Year of Award: </strong>2012</span></span></span></p>
<p><span style="font-size: small;"><span style="font-family: verdana,geneva;"><span style="font-size: small;"><strong>Publication Information:</strong> C<em>ollege Mathematics Journal, </em>vol. 42, no. 1, January 2011, pp. 2-8.</span></span></span></p></div></div></div>A Markov Chain Analysis of the Game of Jai Alai
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-markov-chain-analysis-of-the-game-of-jai-alai
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The game of Jai Alai is used to demonstrate use of Markov chains in modeling.</em></p>
</div></div></div>On the Convergence of the Sequence of Powers of a \(2 \times 2\) Matrix
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-the-convergence-of-the-sequence-of-powers-of-a-2-times-2-matrix
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The fact that the <em>limit of the \(n\)-th power of a \(2\times 2\) matrix \(A\) tends to \(0\) if \( \det A < 1\) and \( \mid 1 + \det(A) \mid > \mid\) tr\( (A) \mid \)</em> is used to prove a well-known theorem in Markov chains for \(2 \times 2\) regular stochastic matrices and to obtain an explicit formula for the stationary matrix and eigenvector.</p>
</div></div></div>Computing the Fundamental Matrix for a Reducible Markov Chain
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/computing-the-fundamental-matrix-for-a-reducible-markov-chain
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>A Markov chain with 9 states is used to illustrate a technique for finding the fundamental matrix.</em></p>
</div></div></div>The Gunfight at the OK Corral
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-gunfight-at-the-ok-corral
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>This article uses a generalization of a three-way gunfight to motivate the construction and solution to a first order linear system of difference equations. The method of undetermined coefficients is used to develop a general solution to the dynamical system. Probabilities of the system converging to each final (absorbing) state are found. According to the author, many mathematical models can be approached from the point of view of discrete dynamical systems.</em></p>
</div></div></div>The Undying Novena
http://www.maa.org/programs/faculty-and-departments/course-communities/the-undying-novena
The Ehrenfest Chains
http://www.maa.org/programs/faculty-and-departments/course-communities/the-ehrenfest-chains
Markov Chains
http://www.maa.org/programs/faculty-and-departments/course-communities/markov-chains
A Random Walk in One Dimension: Applet Demonstration
http://www.maa.org/programs/faculty-and-departments/course-communities/a-random-walk-in-one-dimension-applet-demonstration
Discrete - Time Markov Chains
http://www.maa.org/programs/faculty-and-departments/course-communities/discrete-time-markov-chains
The Disadvantage of Too Much Success.
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-disadvantage-of-too-much-success
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The authors consider three cointossing models in which “too much success” is defined by the occurrence of success runs of a certain length which causes play to stop. The objective is to choose the success probability so as to maximise the expected reward before the stopping time applies.</em></p>
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