Markov processes with free-Meixner laws
نویسندگان
چکیده
منابع مشابه
Noncommutative characterization of free Meixner processes ∗
In this article we give a purely noncommutative criterion for the characterization of free Meixner random variables. We prove that some families of free Meixner distributions can be described in terms of the conditional expectation, which has no classical analogue. We also show a generalization of Speicher’s formula (relating moments and free cumulants) and establish a new relation in free prob...
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In the Black-Scholes option price model Brownian motion and the underlying Normal distribution play a fundamental role. Empirical evidence however shows that the normal distribution is a very poor model to fit real-life data. In order to achieve a better fit we replace the Brownian motion by a special Lévy process: the Meixner process. We show that the underlying Meixner distribution allows an ...
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ABSTRACT. Free Meixner states are a class of functionals on non-commutative polynomials introduced in [Ans06]. They are characterized by a resolvent-type form for the generating function of their orthogonal polynomials, by a recursion relation for those polynomials, or by a second-order non-commutative differential equation satisfied by their free cumulant functional. In this paper, we construc...
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We show that the transition probability of the Markoc chain (G(j, 1),. .. , G(j, n)) j≥1 , where the G(i, j) ′ s are certain directed last-passage times, is given by a determinant of a special form. An analogous formula has recently been obtained by Warren in a Brownian motion model. Furthermore we demonstrate that this formula leads to the Meixner ensemble when we compute the distribution func...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2010
ISSN: 0304-4149
DOI: 10.1016/j.spa.2010.04.006