Related papers: Dirichlet eigenvalues and exit time moments for sy…

We study the exit time $\tau=\tau_{(0,\infty)}$ for 1-dimensional strictly stable processes and express its Laplace transform at $t^\alpha$ as the Laplace transform of a positive random variable with explicit density. Consequently, $\tau$…

We consider a diffusion given by a small noise perturbation of a dynamical system driven by a potential function with a finite number of local minima. The classical results of Freidlin and Wentzell show that the time this diffusion spends…

In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…

We apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage…

The aim of this paper is to investigate how the correlation properties of a stationary Markovian stochastic processes affect the First Passage Time distribution. First Passage Time issues are a classical topic in stochastic processes…

Let $E$ be the class of finite (resp. probability) measures absolutely continuous with respect to a $\sigma$-finite Radon measure on a Polish space. We present a criterion on the quasi-regularity of Dirichlet forms on $E$ in terms of upper…

By using the algebraic construction outlined in \cite{CGRS}, we introduce several Markov processes related to the ${\mathcal{U}}_q(\mathfrak{su}(1,1))$ quantum Lie algebra. These processes serve as asymmetric transport models and their…

First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…

In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition. Firstly, the unique existence and regularity…

We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…

We study Markov chains formed by squared singular values of products of truncated orthogonal, unitary, symplectic matrices (corresponding to the Dyson index $\beta = 1,2,4$ respectively) where time corresponds to the number of terms in the…

We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major…

We consider the symmetric tridiagonal matrix-valued process associated with Gaussian beta ensemble (G$\beta$E) by putting independent Brownian motions and Bessel processes on the diagonal entries and upper (lower)-diagonal ones,…

It is given an effective upper estimate of expectation of |T_1-T_2|, where T_1 and T_2 are the first exit times from a region for two vector diffusion processes.

We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…

This paper studies homogenization of symmetric non-local Dirichlet forms with $\alpha$-stable-like jumping kernels in one-parameter stationary ergodic environment. Under suitable conditions, we establish homogenization results and identify…

The main objective of this article is to compute a first moment for product of Dirichlet and twisted self-dual $GL(3)$ $L$-functions. We discuss the possible simultaneous non vanishing at the central point. We use properties of symmetric…

We investigate toy dynamical models of energy-level repulsion in quantum eigenvalue sequences. We focus on parametric (with respect to a running coupling or "complexity" parameter) stochastic processes that are capable of relaxing towards a…

For a wide class of continuous-time Markov processes, including all irreducible hypoelliptic diffusions evolving on an open, connected subset of $\RL^d$, the following are shown to be equivalent: (i) The process satisfies (a slightly weaker…

Drawdown (resp. drawup) of a stochastic process, also referred as the reflected process at its supremum (resp. infimum), has wide applications in many areas including financial risk management, actuarial mathematics and statistics. In this…