Related papers: Submartingale Condition for Weak Convergence for S…
Weak sharp minimality is a notion emerged in optimization, whose utility is largeley recognized in the convergence analysis of algorithms for solving extremum problems as well as in the study of the perturbation behaviour of such problems.…
The embedding problem for Markov chains is a famous problem in probability theory and only partial results are available up till now. In this paper, we propose a variant of the embedding problem called the reversible embedding problem which…
This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing…
The paper presents new asymptotic recurrent algorithms of phase space reduction for regularly and singularly perturbed semi-Markov processes. These algorithms give effective conditions of weak convergence for distributions and convergence…
We show weak convergence of quantile and expectile processes to Gaussian limit processes in the space of bounded functions endowed with an appropriate semimetric which is based on the concepts of epi- and hypo convergence as introduced in…
In this paper we study Green measures for certain classes of random time change Markov processes where the random time change are inverse subordinators. We show the existence of the Green measure for these processes under the condition of…
This paper studies weak continuity of nonlinear filters. It is well-known that Borel measurability of transition probabilities for problems with incomplete state observations is preserved when the original discrete-time process is replaced…
We consider a recurrent Markov process which is an It\^o semi-martingale. The L\'evy kernel describes the law of its jumps. Based on observations X(0),X({\Delta}),...,X(n{\Delta}), we construct an estimator for the L\'evy kernel's density.…
We exhibit rationally ergodic, weakly mixing measure preserving transformations which are not subsequence rationally weakly mixing and give a condition for smoothness of renewal sequences.
In this note we introduce a new kind of augmentation of filtrations along a sequence of stopping times. This augmentation is suitable for the construction of new probability measures associated to a positive strict local martingale as done…
We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…
This letter derives some new exponential bounds for discrete time, real valued, conditionally symmetric martingales with bounded jumps. The new bounds are extended to conditionally symmetric sub/ supermartingales, and they are compared to…
A new weak bisimulation semantics is defined for Markov automata that, in addition to abstracting from internal actions, sums up the expected values of consecutive exponentially distributed delays possibly intertwined with internal actions.…
In this article we extend the coupling method from classical probability theory to quantum Markov chains on atomic von Neumann algebras. In particular, we establish a coupling inequality, which allow us to estimate convergence rates by…
In the present paper we investigate the $L_1$-weak ergodicity of nonhomogeneous discrete Markov processes with general state spaces. Note that the $L_1$-weak ergodicity is weaker than well-known weak ergodicity. We provide a necessary and…
The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…
Suppose that a real valued process X is given as a solution to a stochastic differential equation. Then, for any twice continuously differentiable function f, the backward Kolmogorov equation gives a condition for f(t,X) to be a local…
We consider a strong Markov process with killing and prove an approximation method for the distribution of the process conditioned not to be killed when it is observed. The method is based on a Fleming-Viot type particle system with…
We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.
A randomised trapezoidal quadrature rule is proposed for continuous functions which enjoys less regularity than commonly required. Indeed, we consider functions in some fractional Sobolev space. Various error bounds for this randomised rule…