Related papers: Approximation of a multivariate conditional densit…

We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the…

We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time $n$. Assuming that the moment of order $2+\delta$ is…

We reduced the large deviation problem for a self-normalized random walk to one for an auxiliary usual bivariate random walk. This enabled us to prove the classical theorem for self-normalized walks by Q.-M. Shao (1997) under slightly more…

We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails…

We clarify the asymptotic of the limsup of the size of the neighborhood of concentration of Sinai's walk improving the result in \cite{Pierre3}. Also we get the almost sure limit of the number of points visited more than a small but fixed…

We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…

A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.

We consider a random walk in random environment in the low disorder regime on $\mathbb Z^d$. That is, the probability that the random walk jumps from a site $x$ to a nearest neighboring site $x+e$ is given by $p(e)+\epsilon \xi(x,e)$, where…

This paper states a law of large numbers for a random walk in a random iid environment on ${\mathbb Z}^d$, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds for the asymptotic velocity of the…

In this paper, we consider the $(1,R)$ state-dependent reflecting random walk (RW) on the half line, allowing the size of jumps to the right at maximal $R$ and to the left only 1. We provide an explicit criterion for positive recurrence and…

A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or…

This is a continuation of our earlier work [Stochastic Processes and their Applications, 129(1), pp.102--128, 2019] on the random walk in random scenery and in random layered conductance. We complete the picture of upper deviation of the…

Consider a transient near-critical (1,2) random walk on the positive half line. We give a criteria for the finiteness of the number of the skipped points (the points never visited) by the random walk. This result generalizes (partially) the…

We consider a one-dimensional random walk $S_n$ with i.i.d. increments with zero mean and finite variance. We study the asymptotic expansion for the tail distribution $\mathbf P(\tau_x>n)$ of the first passage times…

We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…

For a continuous-time random walk $X=\{X_t,t\ge 0\}$ (in general non-Markov), we study the asymptotic behavior, as $t\rightarrow \infty$, of the normalized additive functional $c_t\int_0^{t} f(X_s)ds$, $t\ge 0$. Similarly to the Markov…

We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…

We consider a random walk on $\R^d$ in a polynomially mixing random environment that is refreshed at each time step. We use a martingale approach to give a necessary and sufficient condition for the almost-sure functional central limit…

This elementary treatment first summarizes extreme values of a Bernoulli random walk on the one-dimensional integer lattice over a finite discrete time interval. Both the symmetric (unbiased) and asymmetric (biased) cases are discussed.…