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This article explores an optimal stopping problem for branching diffusion processes. It consists in looking for optimal stopping lines, a type of stopping time that maintains the branching structure of the processes under analysis. By using…
Given a proper convex lower semicontinuous function defined on a Hilbert space and whose solution set is supposed nonempty. For attaining a global minimizer when this convex function is continuously differentiable, we approach it by a…
Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…
We investigate the effective behaviour of a small transversal perturbation of order $\epsilon$ to a completely integrable stochastic Hamiltonian system, by which we mean a stochastic differential equation whose diffusion vector fields are…
Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform…
In this article we propose a Weighted Stochastic Mesh (WSM) Algorithm for approximating the value of a discrete and continuous time optimal stopping problem. We prove that in the discrete case the WSM algorithm leads to semi-tractability of…
This paper proposes novel fixed-time (FXT) convergent neurodynamic approaches for solving mixed variational inequality problems (MVIs). A class of first-order proximal neurodynamic models (PNMs), including time-varying proximal neurodynamic…
In this paper we study the dynamic feedback stability for a simplified model of fluid-structure interaction on a tree. We prove that, under some conditions, the energy of the solutions of the system decay exponentially to zero when the time…
One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience…
We consider nonlocal nonlinear potentials and estimate the rate of convergence of time stepping schemes to the peridynamic equation of motion. We begin by establishing the existence of $H^2$ solutions over any finite time interval. Here…
This report addresses the boundary value problem for a second-order linear singularly perturbed FIDE. Traditional methods for solving these equations often face stability issues when dealing with small perturbation parameters. We propose an…
The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…
We study the optimal stopping time problem $v(S)={\rm ess}\sup_{\theta \geq S} E[\phi(\theta)|\mathcal {F}_S]$, for any stopping time $S$, where the reward is given by a family $(\phi(\theta),\theta\in\mathcal{T}_0)$ \emph{of non negative…
For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time step that is chosen with respect to the background mesh and use the same time step on the…
This paper studies explicitly solvable multidimensional optimal stopping problems of sum- and product-type in discrete and continuous time using the monotone case approach. It gives a review on monotone case stopping using the Doob…
In this paper we propose and analyze an energy stable numerical scheme for the Cahn-Hilliard equation, with second order accuracy in time and the fourth order finite difference approximation in space. In particular, the truncation error for…