相关论文: Non-Markovian random walks with memory lapses

In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…

This paper develops a more general theory of sequences of dependent categorical random variables, extending the works of Korzeniowski (2013) and Traylor (2017) that studied first-kind dependency in sequences of Bernoulli and categorical…

We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suitable conditions on the memory sequence, the arising limiting…

In this paper, we propose a recurrent neural network (RNN) with residual attention (RRA) to learn long-range dependencies from sequential data. We propose to add residual connections across timesteps to RNN, which explicitly enhances the…

Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the…

The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as L{\'e}vy walks for which the persistence times depend on some internal…

Binary data are highly common in many applications, however it is usually modelled with the assumption that the data are independently and identically distributed. This is typically not the case in many real-world examples and such the…

We introduce a new random walk with unbounded memory obtained as a mixture of the Elephant Random Walk and the Dynamic Random Walk which we call the Dynamic Elephant Random Walk (DERW). As a consequence of this mixture the distribution of…

An analysis of free-recall datasets from two independent experiments allows to identify two anomalous instances of non-monotonicity in free recall: a maximum in the dependence of the inter-response intervals on the serial-position lags, and…

There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…

We introduce a new class of asymmetric random walks on the one-dimensional infinite lattice. In this walk the direction of the jumps (positive or negative) is determined by a discrete-time renewal process which is independent of the jumps.…

We consider a class of discrete-time random walks with directed unit steps on the integer line. The direction of the steps is reversed at the time instants of events in a discrete-time renewal process and is maintained at uneventful time…

Ulam has defined a history-dependent random sequence of integers by the recursion $X_{n+1}$ $= X_{U(n)}+X_{V(n)}, n \geqslant r$ where $U(n)$ and $V(n)$ are independently and uniformly distributed on $\{1,\dots,n\}$, and the initial…

Binary time series data are very common in many applications, and are typically modelled independently via a Bernoulli process with a single probability of success. However, the probability of a success can be dependent on the outcome…

We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…

Discovery problems often require deciding whether additional sampling is needed to detect all categories whose prevalence exceeds a prespecified threshold. We study this question under a Bernoulli product (incidence) model, where categories…

Sequential tests and their implied confidence sequences, which are valid at arbitrary stopping times, promise flexible statistical inference and on-the-fly decision making. However, strong guarantees are limited to parametric sequential…

We propose distribution-free runs-based control charts for detecting location shifts. Using the fact that given the number of total successes, the outcomes of a sequence of Bernoulli trials are random permutations, we are able to control…

Infinite sums of i.i.d. random variables discounted by a multiplicative random walk are called perpetuities and have been studied by many authors. The present paper provides a log-type moment result for such random variables under minimal…

The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting…