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We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We…
This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…
We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, time-homogeneous, linear…
In this article, we close a gap in the literature by proving existence of invariant measures for reflected SPDEs with only one reflecting barrier. This is done by arguing that the sequence (u(t, .)) is tight in the space of probability…
Despite significant recent advances in the regularity theory for obstacle problems with integro-differential operators, some fundamental questions remained open. On the one hand, there was a lack of understanding of parabolic problems with…
This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations,…
We study nonnegative, measure-valued solutions to nonlinear drift type equations modelling concentration phenomena related to Bose-Einstein particles. In one spatial dimension, we prove existence and uniqueness for measure solutions.…
We study the problem of existence and uniqueness of solutions of backward stochastic differential equations with two reflecting irregular barriers, $L^p$ data and generators satisfying weak integrability conditions. We deal with equations…
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
This paper is devoted to prove the existence of one or multiple solutions of a wide range of nonlinear differential boundary value problems. To this end, we obtain some new fixed point theorems for a class of integral operators. We follow…
The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod…
We propose an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method…
The Tolman-Oppenheimer-Volkoff (TOV) equation admits singular solutions in addition to regular ones. Here, we prove the following theorem. For any equation of state that (i) is obtained from an entropy function, (ii) has positive pressure…
In this paper, we construct a counterexample to a question by Cantelli, asking whether there exists a nonconstant positive measurable function $\varphi$ such that for i.i.d. r.v. $X,Y$ of law $\mathcal{N}(0,1)$, the r.v. $X+\varphi(X)\cdot…
We prove existence and uniqueness of L^p solutions of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by…
This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…
We consider a reflected backward stochastic differential equations with default time and an optional barrier in a filtration generated by a one-dimensional Brownian motion and a defaultable process. We suppose that the barrier have…
In the present paper we consider the regularizing properties of the repeated midpoint rule for the stable solution of weakly singular Volterra integral equations of the first kind with perturbed right hand sides. The H\"older continuity of…
We present the coisotropic embedding theorem as a tool to provide a solution for the inverse problem of the calculus of variations for a particular class of implicit differential equations, namely the equations of motion of free…
In this paper, we consider reflected anticipated backward stochastic differential equations (RABSDEs, for short) with an additional resistance in the generators. Firstly, we study the existence and uniqueness results. In Luo (2020), the…