scholarly journals Markov Additive Processes II. Large Deviations

1987 ◽  
Vol 15 (2) ◽  
pp. 593-609 ◽  
Author(s):  
P. Ney ◽  
E. Nummelin
Keyword(s):  
Large Deviations ◽  
Additive Processes ◽  
Markov Additive Processes

Continuous-time Markov additive processes: Composition of large deviations principles and comparison between exponential rates of convergence

2001 ◽  
Vol 38 (4) ◽  
pp. 917-931 ◽  
Author(s):  
Claudio Macci
Keyword(s):  
Large Deviations ◽  
Continuous Time ◽  
Fluid Model ◽  
Variational Formula ◽  
Rates Of Convergence ◽  
Rate Function ◽  
Large Deviations Principle ◽  
Additive Process ◽  
Additive Processes ◽  
Markov Additive Processes

We consider a continuous-time Markov additive process (Jt,St) with (Jt) an irreducible Markov chain on E = {1,…,s}; it is known that (St/t) satisfies the large deviations principle as t → ∞. In this paper we present a variational formula H for the rate function κ∗ and, in some sense, we have a composition of two large deviations principles. Moreover, under suitable hypotheses, we can consider two other continuous-time Markov additive processes derived from (Jt,St): the averaged parameters model (Jt,St(A)) and the fluid model (Jt,St(F)). Then some results of convergence are presented and the variational formula H can be employed to show that, in some sense, the convergences for (Jt,St(A)) and (Jt,St(F)) are faster than the corresponding convergences for (Jt,St).

Continuous-time Markov additive processes: Composition of large deviations principles and comparison between exponential rates of convergence

2001 ◽  
Vol 38 (04) ◽  
pp. 917-931 ◽  
Author(s):  
Claudio Macci
Keyword(s):  
Large Deviations ◽  
Continuous Time ◽  
Fluid Model ◽  
Variational Formula ◽  
Rates Of Convergence ◽  
Rate Function ◽  
Large Deviations Principle ◽  
Additive Process ◽  
Additive Processes ◽  
Markov Additive Processes

We consider a continuous-time Markov additive process (J t ,S t ) with (J t ) an irreducible Markov chain on E = {1,…,s}; it is known that (S t /t) satisfies the large deviations principle as t → ∞. In this paper we present a variational formula H for the rate function κ∗ and, in some sense, we have a composition of two large deviations principles. Moreover, under suitable hypotheses, we can consider two other continuous-time Markov additive processes derived from (J t ,S t ): the averaged parameters model (J t ,S t (A)) and the fluid model (J t ,S t (F)). Then some results of convergence are presented and the variational formula H can be employed to show that, in some sense, the convergences for (J t ,S t (A)) and (J t ,S t (F)) are faster than the corresponding convergences for (J t ,S t ).

Large exceedences for uniformly recurrent Markov-additive processes and strong-mixing stationary processes

1995 ◽  
Vol 32 (3) ◽  
pp. 679-691 ◽  
Author(s):  
Tim Zajic
Keyword(s):  
Large Deviations ◽  
Random Variables ◽  
Strong Mixing ◽  
Stationary Processes ◽  
Mixing Processes ◽  
Additive Processes ◽  
Large Deviations Estimates ◽  
Markov Additive Processes

We extend large exceedence results for i.i.d. -valued random variables to a class of uniformly recurrent Markov-additive processes and stationary strong-mixing processes. As in the i.i.d. case, the results are proved via large deviations estimates.

Large exceedences for uniformly recurrent Markov-additive processes and strong-mixing stationary processes

1995 ◽  
Vol 32 (03) ◽  
pp. 679-691
Author(s):  
Tim Zajic
Keyword(s):  
Large Deviations ◽  
Random Variables ◽  
Strong Mixing ◽  
Stationary Processes ◽  
Mixing Processes ◽  
Additive Processes ◽  
Large Deviations Estimates ◽  
Markov Additive Processes

We extend large exceedence results for i.i.d. -valued random variables to a class of uniformly recurrent Markov-additive processes and stationary strong-mixing processes. As in the i.i.d. case, the results are proved via large deviations estimates.

Sign in / Sign up

Export Citation Format

Share Document