Seminario de Probabilidad y Procesos Estocásticos

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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Seminario de Probabilidad y Procesos Estoc&aacute;sticos:</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>El martes 17 de marzo, a las 5 pm,</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>en el Sal&oacute;n 105, Dpto. Matem&aacute;ticas</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Facultad de Ciencias, UNAM, CU:</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Mogens Bladt (IIMAS, UNAM)</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>nos hablar&aacute; sobre:</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Matrix Exponential Methods in Applied Probability</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Resumen:</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>This talk will partly provide an overview of the use of matrix-exponential methods in applied probability, and partly consider some more recent developments where we apply methods from functional calculus to stochastic modeling.</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Matrix-exponential methods have a long history in the theories</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>queueing, risk and telecommunications, and may be considered both from a probabilistic and analytic point of view. In the probabilistic context the distributions which form the basis of the matrix-exponential methods are known as phase-type distributions. A larger and more general class of distributions, which may be considered similarly but without the probabilistic interpretation, is referred to as matrix-exponential distributions.</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>We shall demonstrate how the probabilistic method using phase-type</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>distributions provides a powerful tool for establishing closed form formulas in stochastic modeling. We will consider some examples from renewal theory, ladder heights and risk theory. Finally we introduce the method of functional calculus, which is essentially an elegant way of dealing with functions of matrices, and show how these methods may conveniently be applied to phase-type and matrix-exponential methods.</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Organizan</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Fernando Baltazar</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Sergio L&oacute;pez</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Jos&eacute; Luis P&eacute;rez Garmendia,</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Yuri Salazar</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Ger&oacute;nimo Uribe Bravo</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Correo:</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>P&aacute;gina:</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Para suscribirse a la lista de distribuci&oacute;n entrar a:</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
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<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>y seguir el procedimiento.</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>——————————</span><wbr style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» /><span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>——————————</span><wbr style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» /><span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>—-</span><br style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;» />
<span style=»color: rgb(34, 34, 34); font-family: arial, sans-serif; line-height: normal;»>Webmail, Instituto de Matematicas, UNAM.</span>
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