Related papers: Optimal prediction for positive self-similar Marko…

We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings…

We study a Markov decision problem in which the state space is the set of finite marked point configurations in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the…

We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases…

Let $P$ be the transition matrix of a finite, irreducible and reversible Markov chain. We say the continuous time Markov chain $X$ has transition matrix $P$ and speed $\lambda$ if it jumps at rate $\lambda$ according to the matrix $P$. Fix…

We consider the representation of the value of a class of optimal stopping problems of linear diffusions in a linearized form as an expected supremum of a known function. We establish an explicit integral representation of this representing…

This paper studies small-time behavior at the supremum of a diffusion process. For a solution to the SDE $\mathrm{d} X_t=\mu(X_t)\mathrm{d} t+\sigma(X_t)\mathrm{d} W_t$ (where $W$ is a standard Brownian motion) we consider…

We study the optimal Markovian coupling problem for two Pi-valued Feller processes {X_t} and {Y_t}, which seeks a coupling process {(X_t, Y_t)} that minimizes the right derivative at t = 0 of the expected cost E^{(x,y)}[c(X_t, Y_t)], for…

We give necessary and sufficient conditions for laws of large numbers to hold in $L^2$ for the empirical measure of a large class of branching Markov processes, including $\lambda$-positive systems but also some $\lambda$-transient ones,…

In this paper we study the supremum functional $M_t=\sup_{0\le s\le t}X_s$, where $X_t$, $t\ge0$, is a one-dimensional L\'{e}vy process. Under very mild assumptions we provide a simple, uniform estimate of the cumulative distribution…

We address the algorithmic problem of determining the reversible Markov chain $\tilde X$ that is closest to a given Markov chain $X$, with an identical stationary distribution. More specifically, $\tilde X$ is the reversible Markov chain…

Let $(X_t, Y_t)_{t\in T}$ be a discrete or continuous-time Markov process with state space $X \times R^d$ where $X$ is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component,…

If $X$ is a spectrally positive stable process of index $\alpha\in(1,2)$ whose L\'{e}vy measure has density $cx^{-\alpha-1}$ on $(0,\infty),$ and $S_1=\sup_{0<t\leq1}X_t,$ it is known that $P(S_1>x)\backsim c\alpha^{-1}x^{-\alpha}$ as…

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…

The first motivation of our paper is to explore further the idea that, in risk control problems, it may be profitable to base decisions both on the position of the underlying process Xt and on its supremum Xt := sup 0$\le$s$\le$t Xs.…

Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…

Chi-square processes with trend appear naturally as limiting processes in various statistical models. In this paper we are concerned with the exact tail asymptotics of the supremum taken over (0; 1) of a class of locally stationary…

We study the convergence in distribution of the supremum of the local time and of the favorite site for a transient diffusion in a spectrally negative L\'evy potential. To do so, we study the h-valleys of a spectrally negative L\'evy…

The paper deals with the expected maxima of continuous Gaussian processes $X = (X_t)_{t\ge 0}$ that are H\"older continuous in $L_2$-norm and/or satisfy the opposite inequality for the $L_2$-norms of their increments. Examples of such…

Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…

Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…