Related papers: A pathwise interpretation of the Gorin-Shkolnikov …

It is shown that time reversibility of Hamiltonian microscopic dynamics and Gibbs canonical statistical ensemble of initial conditions for it together produce an exact virial expansion for probability distribution of path of molecular…

The paths of Brownian motion have been widely studied in the recent years relatively in Besov spaces $B_{p, \infty}^\a$. The results are the same as to the Brownian bridge. In fact these regularities properties are established in some…

Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with $n$ faces and boundary component lengths of order $\sqrt n$ or of lower order. Endow this…

We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…

In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows…

In this paper we study the local times of Brownian motion from the point of view of algorithmic randomness. We introduce the notion of effective local time and show that any path which is Martin-L\"of random with respect to the Wiener…

In [O'Connell and Yor (2002)] a path-transformation G was introduced with the property that, for X belonging to a certain class of random walks on the integer lattice, the transformed walk G(X) has the same law as that of the original walk…

We propose a new algorithm to generate a fractional Brownian motion, with a given Hurst parameter, 1/2<H<1 using the correlated Bernoulli random variables with parameter p; having a certain density. This density is constructed using the…

Motivated by [G. Cannizzaro, M. Hairer, Comm. Pure Applied Math., '22], we provide a construction of the Brownian Web (see [T\'oth B., Werner W., Probab. Theory Related Fields, '98] and [L. R. G. Fontes, M. Isopi, C. M. Newman, and K.…

We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by…

In a landscape composed of N randomly distributed sites in Euclidean space, a walker (``tourist'') goes to the nearest one that has not been visited in the last \tau steps. This procedure leads to trajectories composed of a transient part…

We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes till time t. Using a method based on the renewal…

This survey is a collection of various results and formulas by different authors on the areas (integrals) of five related processes, viz.\spacefactor =1000 Brownian motion, bridge, excursion, meander and double meander; for the Brownian…

The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in R\timesR. We extend the earlier work of Arratia and of Toth and Werner by…

We derive asymptotics for the probability of the origin to be an extremal point of a random walk in R^n. We show that in order for the probability to be roughly 1/2, the number of steps of the random walk should be between e^{c n / log n}$…

Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that…

We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph $G$, and present a formula for the characteristic polynomial of the transition probability matrix of this CRW…

A class of Gaussian processes generalizing the usual fractional Brownian motion for Hurst indices in (1/2,1) and multifractal Brownian motion introduced in Ralchenko and Shevchenko (Theory Probab Math Stat 80, 2010) and Boufoussi et al.…

In this article, we show a result of approximation in law to subfractional Brownian motion, with $H>\frac{1}{2}$, in the Skorohod topology. The construction of these approximations is based on a sequence of I.I.D random variables

We supplement a very recent paper of G. Markowsky concerned with the expected exit times of Brownian motion from planar domains. Besides the use of conformal mapping, we apply results from potential theory. We treat the case of a…