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We consider a discrete-time Markov chain $boldsymbol{Phi}$ on a general state-space ${sf X}$, whose transition probabilities are parameterized by a real-valued vector $boldsymbol{theta}$. Under the assumption that $boldsymbol{Phi}$ is geometrically ergodic with corresponding stationary distribution $pi(boldsymbol{theta})$, we are interested in estimating the gradient $ abla alpha(boldsymbol{theta})$ of the steady-state expectation $$alpha(boldsymbol{theta}) = pi( boldsymbol{theta}) f.$$ To this end, we first give sufficient conditions for the differentiability of $alpha(boldsymbol{theta})$ and for the calculation of its gradient via a sequence of finite horizon expectations. We then propose two different likelihood ratio estimators and analyze their limiting behavior.
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration inequalities su
We present a novel technique for estimating disk parameters (the centre and the radius) from its 2D image. It is based on the maximal likelihood approach utilising both edge pixels coordinates and the image intensity gradients. We emphasise the follo
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i in [0, 1]$ drawn from some unknown distribution $P^star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i sim text{Binomial}(t, p_i
The mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model, has been widely used in modelling volatility, interest rate and exchange rate. Obviously, if some phenomenon are modeled by the mixed fractional Vasicek
We analyze an interacting queueing network on $mathbb{Z}^d$ that was introduced in Sankararaman-Baccelli-Foss (2019) as a model for wireless networks. We show that the marginals of the minimal stationary distribution have exponential tails. This is u