We propose a method to construct the stochastic integral simultaneously under a non-dominated family of probability measures. Path-by-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes integrals whose medial limit coincides with the usual stochastic…

Symmetry properties of the random grid spanned on the set of records from the planar Poisson point process imply bizarre multivariate distributional identities for certain rational functions of independent exponential and uniform random variables.

We consider a version of a classical concentration inequality for sums of independent, isotropic random vectors with a mild restriction on the distribution of the radial part of these vectors. The proof uses a little Fourier analysis, the Laplace asymptotic method and a…

We consider a class of real random matrices with dependent entries and show that the limiting empirical spectral distribution is given by the Marchenko-Pastur law. Additionally, we establish a rate of convergence of the expected empirical spectral distribution.

We prove  weak convergence of sums over triangular arrays to the compound Poisson limit using Tikhomirov's method.  The result is applied to statistical estimation of the threshold  parameter in autoregressive models.

We consider the Cheeger constant $\phi(n)$ of the giant component of supercritical bond percolation on $\mathbb{Z}^d/n\mathbb{Z}^d$. We show that the variance of $\phi(n)$ is bounded by $\frac{\xi}{n^d}$, where $\xi$ is a positive constant that depends only on the dimension $d$…

We establish the existence and uniqueness ofstrong solutions to some jump-type stochastic equations under non-Lipschitz conditions. The results improve those of Fu and Li (2010) and Li and Mytnik (2011).

This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, then the empirical distribution of the critical points of $p_n$ converges weakly…

We prove that the multi-time particle distributions for annihilating or coalescing Brownian motions, under the maximal entrance law on the real line, are extended Pfaffian point processes.

It is shown that if a planar graph admits no non-constant bounded harmonic function then the trajectories of two independent simple random walks  intersect almost surely.