On the limit laws of the second order for additive functionals of Harris recurrent Markov chains

2000 ◽  
Vol 116 (1) ◽  
pp. 89-123 ◽  
Author(s):  
Xia Chen
Keyword(s):  
Markov Chains ◽  
Second Order ◽  
Limit Laws ◽  
Additive Functionals

scholarly journals Second-order limit laws for occupation times of fractional Brownian motion

2017 ◽  
Vol 54 (2) ◽  
pp. 444-461 ◽  
Author(s):  
Fangjun Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Method Of Moments ◽  
Second Order ◽  
Hurst Index ◽  
Occupation Times ◽  
Limit Laws ◽  
Additive Functionals ◽  
Finite Dimensional ◽  
Functional Version

Abstract We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1 / d, using the method of moments and extending the Kallianpur–Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

On the invariance principle for reversible Markov chains

2016 ◽  
Vol 53 (2) ◽  
pp. 593-599 ◽  
Author(s):  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Standard Deviation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Markov Chains ◽  
Stochastic Processes ◽  
Partial Sums ◽  
Additive Functionals ◽  
Functional Clt ◽  
Reversible Markov Chains ◽  
Functional Central Limit

Abstract In this paper we investigate the functional central limit theorem (CLT) for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation of partial sums. For this case, we show that the functional CLT is equivalent to the fact that the variance of partial sums is regularly varying with exponent 1 and the partial sums satisfy the CLT. It is also equivalent to the conditional CLT.

scholarly journals Some variational formulas on additive functionals of symmetric Markov chains

2001 ◽  
Vol 130 (7) ◽  
pp. 2115-2123 ◽  
Author(s):  
Daehong Kim ◽  
Masayoshi Takeda ◽  
Jiangang Ying
Keyword(s):  
Markov Chains ◽  
Additive Functionals ◽  
Variational Formulas

Use of second order Markov chains to model digital symbol synchroniser performance

1996 ◽  
Vol 143 (5) ◽  
pp. 250 ◽  
Author(s):  
D.W. Paranchych ◽  
N.C. Beaulieu
Keyword(s):  
Markov Chains ◽  
Second Order ◽  
Digital Symbol

Classification of Encrypted Traffic With Second-Order Markov Chains and Application Attribute Bigrams

2017 ◽  
Vol 12 (8) ◽  
pp. 1830-1843 ◽  
Author(s):  
Meng Shen ◽  
Mingwei Wei ◽  
Liehuang Zhu ◽  
Mingzhong Wang
Keyword(s):  
Markov Chains ◽  
Second Order ◽  
Encrypted Traffic
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