Related papers: Markov selection for constrained martingale proble…
This work introduces the extended Skorokhod problem (ESP) and associated extended Skorokhod map (ESM) that enable a pathwise construction of reflected diffusions that are not necessarily semimartingales. Roughly speaking, given the closure…
Under suitable assumptions of regularity and non-degeneracy on the covariance of the driving additive noise, any Markov solution to the stochastic Navier-Stokes equations has an associated generator of the diffusion and is the unique…
We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition. Further, the process is…
In this article integro-differential Volterra equations whose convolution kernel depends on the vector variable are considered and a connection of these equations with a class of semi-Markov processes is established. The variable order…
The focus of this article is studying an optimal control problem for branching diffusion processes. Initially, we introduce the problem in its strong formulation and expand it to include linearly growing drifts. Then, we present a relaxed…
We establish circumstances under which the dispersion of passive contaminants in a forced, deterministic or random, flow can be consistently interpreted as a Markovian diffusion process. In case of conservative forcing the repulsive case…
We provide several characterizations to identify Strong envelop (for bounded measurable process) and Strong super-martingale (for non-negative right upper semi-continuous process of the class $\Dc$). As examples of application, we prove…
In this paper, we study darning of general symmetric Markov processes by shorting some parts of the state space into singletons. A natural way to construct such processes is via Dirichlet forms restricted to the function space whose members…
In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…
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…
This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the…
Let $X$ be a Markov process taking values in $\mathbf{E}$ with continuous paths and transition function $(P_{s,t})$. Given a measure $\mu$ on $(\mathbf{E}, \mathscr{E})$, a Markov bridge starting at $(s,\varepsilon_x)$ and ending at…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
We compare numerically the performance of reversible and non-reversible Markov Chain Monte Carlo algorithms for high dimensional oil reservoir problems; because of the nature of the problem at hand, the target measures from which we sample…
It was recently proven that the correlation function of the stationary version of a reflected L\'evy process is nonnegative, nonincreasing and convex. In another branch of the literature it was established that the mean value of the…
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…
Comparison results are given for time-inhomogeneous Markov processes with respect to function classes induced stochastic orderings. The main result states comparison of two processes, provided that the comparability of their infinitesimal…
We study the large deviations of time-integrated observables of Markov diffusions that have perfectly reflecting boundaries. We discuss how the standard spectral approach to dynamical large deviations must be modified to account for such…
Conditions on the generator of a Markov process to control the fluctuations of its bridges are found. In particular, continuous time random walks on graphs and gradient diffusions are considered. Under these conditions, a concentration of…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…