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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

0 votes
1 answer
161 views

Extracting moments from a special Z-transform

Suppose I have a sequence of positive continuous random variables $\{X_k\}_{k=1}^\infty$ with (unknown) MGF's $M_{X_k}(s)$. Furthermore, it is known that \begin{equation}\frac{X_n-n\mu}{\sqrt{n}\sigma …
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2 votes
0 answers
199 views

CLT for a Markov Renewal Process

Suppose $(X,T)=\{(X_n,T_n)\}_{n\geq0}$ is a Markov renewal process, where $X$ is a finite-state, discrete-time Markov chain with state space $\{1,2,...,R\}$. $T$ is the additive component, more precis …
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