V. Anantharam, T. Konstantopoulos, Stationary solutions of stochastic recursions describing discrete event systems, Stochastic Processes and Their Applications 68 (1997) 181--194, correction published in vol. 80, no. 2, pp. 271-- 278, April 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....5.5 are necessary and sufficient for strong coupling convergence. Let V be a compact subset of E. The conditions of Theorem 5.6 are necessary and sufficient for strong coupling convergence uniformly over initial conditions in V . Next theorem was proved by Anantharam and Konstantopoulos in [1]. Theorem 5.8. F ; P ) be a probability space. We assume that( Omega ; F) is a Polish space equipped with its Borel oe algebra. We consider a SRS x(n 1) f(x(n) a(n) defined on E. Suppose that, for some x 0 2 E, the sequence fx(n; x 0 )g is tight on E. Then there is a stationary ....

....defined on E. Suppose that, for some x 0 2 E, the sequence fx(n; x 0 )g is tight on E. Then there is a stationary distribution for the SRS. The stationary distribution is defined Theta E with an Omega marginal equal to P . It provides only a weak stationary regime (wsr) for the SRS, see [1] or [13] for details. All we need to know about wsr is that stationary regimes are wsr. Hence, the uniqueness of stationary regimes implies the uniqueness of wsr. It is proved in [10] that for an i.i.d. SRS (i.e. Markov chain) the conditions of Th. 5.5 are equivalent to the ones ensuring Harris ....

V. Anantharam and T. Konstantopoulos. Stationary solutions of stochastic recursions describing discrete event systems. In Proc. 33rd Conf. on Decision and Control, volume 2, pages 1481--1486, Lake Buena Vista, FL, 1994.

....The matrix F is diagonal with F = fI , 0 f 1; and Q 0. A4 The joint family of random variables fP k ; k ; e k g admits a stationary solution, with P k = E[ k 1 T k 1 j Y k ] When f 1, assumptions (A1) A3) imply that (A4) is automatically satisfied (using the result of [1]) Under a persistence of excitation condition, A4) holds even with f = 1 (combine the main results of [10] and [1] Assumption (A3) that F is diagonal is not strictly required. The results presented here will continue to hold if F I . Thus it is possible to treat hybrid situations where some ....

.... ; e k g admits a stationary solution, with P k = E[ k 1 T k 1 j Y k ] When f 1, assumptions (A1) A3) imply that (A4) is automatically satisfied (using the result of [1] Under a persistence of excitation condition, A4) holds even with f = 1 (combine the main results of [10] and [1]) Assumption (A3) that F is diagonal is not strictly required. The results presented here will continue to hold if F I . Thus it is possible to treat hybrid situations where some parameters are time varying and others are not. This general situation is treated in [24] Define the steady state ....

V. Anantharam and T. Konstantopoulos. Stationary solutions of stochastic recursions describing discrete event systems. In Proceedings of the 33st IEEE Conference on Decision and Control, pages 1481--1486, Orlando, FL, December 1994.

....5.5 are necessary and sufficient for strong coupling convergence. Let V be a compact subset of E. The conditions of Theorem 5.6 are necessary and sufficient for strong coupling convergence uniformly over initial conditions in V . Next theorem was proved by Anantharam and Konstantopoulos in [1]. Theorem 5.8. Let( Omega ; F ; P ) be a probability space. We assume that( Omega ; F) is a Polish space equipped with its Borel oe algebra. We consider a SRS x(n 1) f(x(n) a(n) defined on E. Suppose that, for some x 0 2 E, the sequence fx(n; x 0 )g is tight 2 on E. Then there is a ....

....on E. Suppose that, for some x 0 2 E, the sequence fx(n; x 0 )g is tight 2 on E. Then there is a stationary distribution for the SRS. The stationary distribution is defined on Omega Theta E with an Omega marginal equal to P . It provides only a weak stationary regime (wsr) for the SRS, see [1] or [13] for details. All we need to know about wsr is that stationary regimes are wsr. Hence, the uniqueness of stationary regimes implies the uniqueness of wsr. It is proved in [10] that for an i.i.d. SRS (i.e. Markov chain) the conditions of Th. 5.5 are equivalent to the ones ensuring ....

V. Anantharam and T. Konstantopoulos. Stationary solutions of stochastic recursions describing discrete event systems. In Proc. 33rd Conf. on Decision and Control, volume 2, pages 1481--1486, Lake Buena Vista, FL, 1994.

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Anantharam, V. and Konstantopoulos, T. (1999) A correction and some additional remarks on: "stationary solutions of stochastic recursions describing discrete event systems". Stoch. Proc. Appl. 80, 271-278.

....when q is small, and when q is large. More precisely, we find that 0 (heavy graph) O( 1 q) log(1 q) as q 1 (sparse graph) In addition, we present a functional law of large numbers for the infinite bin model (Theorem 7) which states that t, as n , uniformly in t [0, 1], a.s. We complement this result by a corresponding central limit theorem (Theorem 8) stating that # # # # t#0 BROWNIAN MOTION , as n denotes weak convergence in D[0, #) with the topology of uniform convergence on compacta, provided that we introduce some independence ....

....random memory. Consider a process Z with values in a Polish space S and suppose that its transition kernel, defined by P (X n X n 1 , X n 2 , is time homogeneous [a similar setup is considered in the paper by Comets et al. 2001) i.e. that there exists a kernel : K # B(K) [0, 1] such that P (X n X n 1 , X n 2 , X n 1 , X n 2 , B) B B(K) This represents the dynamics of the process. In addition, assume that the dynamics does not depend on the whole past, but on a finite but random number of random variables from the past. It is also required that ....

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Anantharam, V. and Konstantopoulos, T. (1997) Stationary solutions of stochastic recursions describing discrete event systems. Stoch. Proc. Appl. 68, 181-194.

....restilt m the sin ale server quoue, which corresponds to finding a st.ationary solution for the Lindley equation. Our point. 1482 of view is such that the monotonicity in the Lind ley equation is not appealed to; tbr lack of space we have not explicated this further here, for details see [1]. We point out the interesting fact that a station ary recursion on a compact state space always admits a stationary solution in our sense. In Section 4, we discuss the question of uniqueness of station ary solutions. Here we give a theorem on uniqueness along lines familiar from the ergodie ....

....theory of positive Markov operators on spaces of continuous functions see, for instance, Krengel [12, Chapter 5] In Section 5 we demonstrate how the uniqueness theorem can be used to establish uniqueness of solutions in the problem of the single server queue. More examples are discussed in [1], but could not be included here. Some concluding remarks are made in Section 6. 2 Existence of stationary solu tions Suppose x, n 0 is a stationary solution to (1) In other words, this is a stationary sequence on the original probability space (f) jr, p) and can thus be termed a strong ....

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Anantharam, V. and Konstantopoulos, T. (1994). Stationary solutions of stochastic recursions describing discrete event systems. Tech. Rep. SCC-9-03, ECE Dept., Univ. of Texas at Austin.

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V. Anantharam, T. Konstantopoulos, Stationary solutions of stochastic recursions describing discrete event systems, Stochastic Processes and Their Applications 68 (1997) 181--194, correction published in vol. 80, no. 2, pp. 271-- 278, April 1999.

No context found.

V. Anantharam, T. Konstantopoulos, Stationary solutions of stochastic recursions describing discrete event systems, Stochastic Processes and Their Applications 68 (1997) 181--194, correction published in vol. 80, no. 2, pp. 271-- 278, April 1999.

No context found.

V. Anantharam and T. Konstantopoulos, "Stationary Solutions of Stochastic Recursions describing Discrete Event Systems", Stochastic Processes and Their Applications, Vol. 68, pp. 181-194, 1997.

No context found.

V. Anantharam and T. Konstantopoulos, "Stationary Solutions of Stochastic Recursions describing Discrete Event Systems", Stochastic Processes and Their Applications, Vol. 68, pp. 181-194, 1997.

No context found.

V. Anantharam and T. Konstantopoulos, "Stationary Solutions of Stochastic Recursions describing Discrete Event Systems", Stochastic Processes and Their Applications, Vol. 68, pp. 181-194, 1997.

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