Related papers: Persistence problems for additive functionals of o…

We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…

We study the properties of the exponential functional $\int\_0^{+ \infty} e^{- X^{\uparrow} (t)}dt$ where $X^{\uparrow}$ is a spectrally one-sided L{\'e}vy process conditioned to stay positive. In particular, we study finiteness,…

This note develops shortly the theory of time-inhomogeneous additive functionals and is a useful support for the analysis of time-dependent Markov processes and related topics. It is a significant tool for the analysis of BSDEs in law. In…

Let X and Y be time-homogeneous Markov processes with common state space E, and assume that the transition kernels of X and Y admit densities with respect to suitable reference measures. We show that if there is a time t>0 such that, for…

Let $X$ be an irreducible symmetric Markov process with the strong Feller property. We assume, in addition, that $X$ is explosive and has a tightness property. We then prove the existence and uniqueness of quasi-stationary distributions of…

We examine two analytical characterisation of the metastable behavior of a Markov chain. The first one expressed in terms of its transition probabilities, and the second one in terms of its large deviations rate functional. Consider a…

The time at which a one-dimensional continuous strong Markov process attains a boundary point of its state space is a discontinuous path functional and it is, therefore, unclear whether the exit time can be approximated by hitting times of…

For AR(1)-processes $X_n=\rho X_{n-1}+\xi_n$, $n\in\mathbb{N}$, where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\in\mathbb{N}}$ is an i.i.d. sequence of random variables, we study the persistence probabilities $\mathbb{P}(X_0\ge 0,\dots, X_N\ge…

We consider a sequence of additive functionals {\phi_n}, set on a sequence of Markov chains {X_n} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms…

We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with…

We consider the problem of absolute continuity for the one-dimensional SDE \[X_t=x+\int_0^ta(X_s) ds+Z_t,\] where $Z$ is a real L\'{e}vy process without Brownian part and $a$ a function of class $\mathcal{C}^1$ with bounded derivative.…

We introduce a parameter $p$, called partial survival, in the persistence of stochastic processes and show that for smooth processes the persistence exponent $\theta(p)$ changes continuously with $p$, $\theta(0)$ being the usual persistence…

Let $\tau(x)$ be the first time the reflected process $Y$ of a Levy processes $X$ crosses x>0. The main aim of the paper is to investigate the asymptotic dependence of the path functionals: $Y(t) = X(t) - \inf_{0\leq s\leq t}X(s)$,…

This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…

Let $X_t^\sharp$ be a multivariate process of the form $X_t =Y_t - Z_t$, $X_0=x$, killed at some terminal time $T$, where $Y_t$ is a Markov process having only jumps of the length smaller than $\delta$, and $Z_t$ is a compound Poisson…

Suppose the auto-correlations of real-valued, centered Gaussian process $Z(\cdot)$ are non-negative and decay as $\rho(|s-t|)$ for some $\rho(\cdot)$ regularly varying at infinity of order $-\alpha \in [-1,0)$. With $I_\rho(t)=\int_0^t…

For real-valued additive process $(X\_t)\_{t\geq 0}$ a recursive equation is derived for the entire positive moments of functionals $$I\_{s,t}= \int \_s^t\exp(-X\_u)du, \quad 0\leq s<t\leq\infty, $$ in case the Laplace exponent of $X\_t$…

In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation…

In this article, we introduce an infinite-dimensional analogue of the $\alpha$-stable L\'evy motion, defined as a L\'evy process $Z=\{Z(t)\}_{t \geq 0}$ with values in the space $\mathbb{D}$ of c\`adl\`ag functions on $[0,1]$, equipped with…

We study nonlinear time-inhomogeneous Markov processes in the sense of McKean's seminal work [32]. These are given as families of laws $\mathbb{P}_{s,\zeta}$, $s\geq 0$, on path space, where $\zeta$ runs through a set of admissible initial…