• Corpus ID: 252567842

Non-local Boundary Value Problems for Brownian motions on the half line

  title={Non-local Boundary Value Problems for Brownian motions on the half line},
  author={Fausto Colantoni and Mirko D’Ovidio},
. We study boundary value problems involving non-local operators for the dynamic boundary conditions. Our analysis includes a detailed description of such operators together with their relations with random times and random functionals. We provide some new characterizations for the boundary behaviour of the Brownian motion based on the interplay between non-local operators and boundary value problems. 
1 Citations

Figures from this paper

On the Non-Local Boundary Value Problem from the Probabilistic Viewpoint

We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators



Fractional Boundary Value Problems and Elastic Sticky Brownian Motions

Sticky diffusion processes spend finite time (and finite mean time) on a lower-dimensional boundary. Once the process hits the boundary, then it starts again after a random amount of time. While on the

Time fractional equations and probabilistic representation

A boundary property of semimartingale reflecting Brownian motions

SummaryWe consider a class of reflecting Brownian motions on the non-negative orthant inRK. In the interior of the orthant, such a process behaves like Brownian motion with a constant covariance

Traps for reflected Brownian motion

Consider an open set , d ≥ 2, and a closed ball . Let denote the expectation of the hitting time of B for reflected Brownian motion in D starting from x ∈ D. We say that D is a trap domain if . A

Fractional equations via convergence of forms

Abstract We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by

Reflected Brownian Motion on an Orthant

We consider a K-dimensional diffusion process Z whose state space is the nonnegative orthant. On the interior of the orthant, Z behaves like a Kdimensional Brownian motion with arbitrary covariance

Fractional Poisson process with random drift

We study the connection between PDEs and Levy processes running with clocks given by time-changed Poisson processes with stochastic drifts. The random times we deal with are therefore given by

Lévy processes and infinitely divisible distributions

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5.

Full characterization of the fractional Poisson process

The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in

Markov Processes, Semigroups and Generators

Part I Brownian Motion, Markov Processes, Martingales. 1 Preliminaries in Probability and Analysis. 2 Browninan Motion I: Constructions. 3 Martingales and Markov Processes. 4 Browninan Motion II: