Related papers: Conditional limit theorems for regulated fractiona…

The conditional expectation and conditional variance of Brownian motion is considered given the argmax, B(t|argmax), as well as those with additional information: B(t|close, argmax), B(t|max, argmax), B(t|close, max, argmax) where the close…

We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H>1/2 as a typical example. We establish infinite and finite past…

We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give series expansions…

Let $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type \[X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^t\mu\bigl(X(u)\bigr)\mathrm…

We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes have been established recently in literature with novel objects appearing in the limits. In…

The paper presents a phenomenon occurring in population processes that start near zero and have large carrying capacity. By the classical result of Kurtz~(1970), such processes, normalized by the carrying capacity, converge on finite…

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…

In this paper, we analyze a two-queue random time-limited Markov modulated polling model. In the first part of the paper, we investigate the fluid version: Fluid arrives at the two queues as two independent flows with deterministic rate.…

We consider the asymptotic behavior of the KPZ fixed point $\{\mathsf H(x,t)\}_{x\in\mathbb R, t>0}$ conditioned on $\mathsf H(0,T)=L$ as $L$ goes to infinity. The main result is a conditional limit theorem for the fluctuations of $\mathsf…

This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…

A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work,…

We consider a system of $N$ non-crossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we…

We provide upper and lower bounds for the mean ${\mathscr M}(H)$ of $\sup_{t\geqslant 0} \{B_H(t) - t\}$, with $B_H(\cdot)$ a zero-mean, variance-normalized version of fractional Brownian motion with Hurst parameter $H\in(0,1)$. We find…

This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The…

Here we review and extend central limit theorems for highly chaotic but deterministic semi-dynamical discrete time systems. We then apply these results show how Brownian motion-like results are recovered, and how an Ornstein-Uhlenbeck…

We study a many-server queuing system with general service time distribution and state dependent service rates. The dynamics of the system are modeled using measure valued processes which keep track of the residual service times. Under…

This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated…

We study the occupation fluctuations of drifted Brownian motion in a closed interval, and show that they undergo a dynamical phase transition in the long-time limit without an additional low-noise limit. This phase transition is similar to…

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service…

In this paper we argue that boundary condition may run with energy scale. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin.…