Related papers: A Strong Law of Large Numbers for Strongly Mixing …
We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process which is strongly H\"older continuous in time, then this sequence converges in the strong sense even…
We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We…
We introduce a class of Adapted Increasingly Rarely Markov Chain Monte Carlo (AirMCMC) algorithms where the underlying Markov kernel is allowed to be changed based on the whole available chain output but only at specific time points…
We derive strong mixing conditions for many existing discrete-valued time series models that include exogenous covariates in the dynamic. Our main contribution is to study how a mixing condition on the covariate process transfers to a…
For the partial sums formed from a sequence of i.i.d. random variables having a finite absolute p'th moment for some p in (0,2), we extend the recent and striking discovery of Hechner and Heinkel (Journal of Theoretical Probability (2010))…
The validity of the strong law of large numbers for multiple sums $S_n$ of independent identically distributed random variables $Z_k$, $k\leq n$, with $r$-dimensional indices is equivalent to the integrability of $|Z|(\log^+|Z|)^{r-1}$,…
In this paper, we obtain almost sure invariance principles with rate of order $n^{1/p}\log^\beta n$, $2< p\le 4$, for sums associated to a sequence of reverse martingale differences. Then, we apply those results to obtain similar…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (larger states shift up transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained using order-theoretic…
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…
We study a mutliscale jump process introduced in a work by Crudu, Debussche, Muller and Radulescu. Using an adequate coupling, we are able to prove the strong convergence, for the uniform topology, to a piecewise deterministic Markov…
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
Time in-homogeneous cyclic Markov chain Monte Carlo (MCMC) samplers, including deterministic scan Gibbs samplers and Metropolis within Gibbs samplers, are extensively used for sampling from multi-dimensional distributions. We establish a…
We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…
We suggest an approach to obtaining general two-sided bounds on the rate of convergence in terms of special "weighted" norms related to total variation. Some important classes of continuous-time Markov chains are considered:…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's…
If you take a superposition of n IID copies of a point process and thin that by a factor of 1/n, then the resulting process tends to a Poisson point process as n tends to infinity. We give a simple proof of this result that highlights its…
In this paper, we obtain precise rates of convergence in the strong invariance principle for stationary sequences of real-valued random variables satisfying weak dependence conditions including strong mixing in the sense of Rosenblatt…
We establish a strong law of large numbers under intermediate trimming for a particular example of Birkhoff sums of a non-integrable observable over the doubling map. It has been shown in a previous work by Haynes that there is no strong…