Kesten, H. (1973). Random di erence equations and renewal theory for products of random matrices. Acta Math. 131, 207-248. Home/Search Document Not in Database Summary Related Articles Check |
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Renewal theory for functionals of a Markov chain with .. - Klüppelberg.. (2001) (Correct)
....and process respectively. Here j j denotes any norm in R . In the one dimensional case (q = 1) Goldie [8] has solved the problem in a very elegant way and found the tail behaviour (1.3) But for the multivariate model (q 1) renewal theory is called for. One can show (see, for example, Kesten [13] and Le Page [18] that the function P(x Y t) is asymptotically equivalent to a renewal function, that is Y t) G(x; t) E x g(x n ; t v n ) t 1 ; 1.4) where means that the quotient of both sides tends to 1. Here g( is some continuous function satisfying condition (2.4) ....
....theorem one has to check a direct Riemann integrability condition for the function g( see Kesten [14] equation (1.11) This is a dicult task because it requires the explicit form of the in nite distributions of the processes (1.5) and (1. 6) For matrices with non negative elements Kesten [13] proved that his notion of direct Riemann integrablity is equivalent to our condition (2.4) below, which is in general weaker than Kesten s condition. Since models like ARCH(1) and GARCH(1,1) play a prominent role as volatility models in nance, which are by nature positive, Kesten s results ....
Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrixes. Acta. Math. 131, 207-248.
Risk Management with Extreme Value Theory - Klüppelberg (2002) (Correct)
....2e , where is Euler s constant. The tail of the stationary distribution is known to be Pareto like (see e.g. Goldie [41] or EKM [33] Section 8. 4) This result was obtained by considering the square ARCH(1) process leading to a stochastic recurrence equation which ts in the setting of Kesten [53, 54] and Vervaat [88] see also Diaconis and Freedman [26] for an interesting overview and Brandt, Franken and Lisek [19] Goldie and Maller [42] give necessary and sucient conditions for stationarity of stochastic processes, which are solutions of stochastic recurrence equations. For the general case ....
....type arguments, by invoking the Drasin Shea Tauberian theorem. This approach has the drawback that it ensures regular variation of the stationary tail, but gives no information on the slowly varying function. However, the method does apply to processes which do not t into the framework of Kesten [53]. Moreover, the Tauberian approach does not depend on additional assumptions which are often very hard to check (as e.g. the existence of certain moments of the stationary distribution) Combining the Tauberian method with results in Goldie [41] we nally specify the slowly varying function as a ....
Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrixes. Acta Math. 131, 207-248.
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Kesten, H. (1973). Random di erence equations and renewal theory for products of random matrices. Acta Math. 131, 207-248.
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Kesten, H. (1973). Random di#erence equations and renewal theory for products of random matrices, Acta Math. 131: 207--248.
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Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrices. Acta Math. 131, 207-248.
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Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrixes. Acta Math., 131, 207-248.
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Kesten, H. (1973) Random di#erence equations and renewal theory for products of random matrices. Acta Math. 131, 207-248.
Risk Management with Extreme Value Theory - Klüppelberg (2002) (Correct)
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Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrixes. Acta Math. 131, 207-248.
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Kesten, H. (1973). Random di#erence equations and renewal theory for product of random matrices. Acta Math. 131 207-248.
Renewal theory for functionals of a Markov chain with .. - Klüppelberg.. (2002) (Correct)
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Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrixes. Acta. Math. 131, 207-248.
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Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrices. Acta Math. 131, 207-248.
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Kesten, H (1973), "Random di#erence equations and renewal theory for products of random matrices," Acta Mathematica, CXXXI: 207-248.
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Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrices. Acta Math. 131, 207-248.
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Kesten, H. (1973). Random di#erence equations and renewal theory for products of random matrices. Acta Math. 131, 207--248. 29
The tail of the stationary distribution of a random.. - Klüppelberg.. (2001) (Correct)
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Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrixes. Acta Math., 131, 207-248.
The tail of the stationary distribution of a random coefficient .. - Klüppelberg (2001) (Correct)
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Kesten, H. (1973) Random di erence equations and renewal theory for products of random matrixes. Acta Math., 131, 207-248.
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