Displaying similar documents to “Corrections to “On Lev́y processes conditioned to stay positive'.”

Potentials of a Markov process are expected suprema

Hans Föllmer, Thomas Knispel (2007)

ESAIM: Probability and Statistics

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Expected suprema of a function  observed along the paths of a nice Markov process define an excessive function, and in fact a potential if  vanishes at the boundary. Conversely, we show under mild regularity conditions that any potential admits a representation in terms of expected suprema. Moreover, we identify the maximal and the minimal representing function in terms of probabilistic potential theory. Our results are motivated by the work of El Karoui and Meziou (2006) on the max-plus...

Absorption in stochastic epidemics

Josef Štěpán, Jakub Staněk (2009)

Kybernetika

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A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack–McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.