Related papers: The Skorohod oblique reflection problem in time-de…
A reflection map, induced by the deterministic Skorohod problem on the nonnegative orthant, is applied to an $\mathbb{R}^n$ valued function $X$ on $[0,\infty)$ and then to $a+X$, where $a$ is a nonnegative constant vector. A question that…
This paper develops a time-inconsistent and path-dependent singular control framework incorporating a running minimum process. We derive a verification theorem that characterizes equilibria under substantially weaker regularity conditions…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
In this paper we consider the Stratonovich reflected stochastic differential equation $dX_t=\sigma(X_t)\circ dW_t+b(X_t)dt+dL_t$ in a bounded domain $\O$ which satisfies conditions, introduced by Lions and Sznitman, which are specified…
This paper is concerned with a wave equation in dimension $d\in \{1,2, 3\}$, with a multiplicative space-time Gaussian noise which is fractional in time and homogeneous in space. We provide necessary and sufficient conditions on the…
This paper investigates a time-dependent multidimensional stochastic differential equation with drift being a distribution in a suitable class of Sobolev spaces with negative derivation order. This is done through a careful analysis of the…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
We prove the existence of strong solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey spaces. Strong uniqueness is also discussed.
In the recent papers [Lochowski:2011fk, Lochowski:2013yq, Lochowski:2013lr] the truncated variation has been introduced, characterized and studied in various stochastic settings. In this note we uncover an intimate link to the Skorokhod…
Processes which arise as solutions to stochastic differential equations involving the local time (SDELTs), such as skew Brownian motion, are frequent sources of inspiration in theory and applications. Existence and uniqueness results for…
We present simple assumptions on the constraints defining a hard core dynamics for the associated reflected stochastic differential equation to have a unique strong solution. Time-reversibility is proven for gradient systems with normal…
The article deals with existence and uniqueness of the solution of the following differential equation (a c\`adl\`ag Skorokhod problem) driven by a maximal monotone operator and with singular input generated by the c\`{a}dl\`{a}g function…
Population dynamics with complex biological interactions, accounting for uncertainty quantification, is critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the…
In this paper we will study the existence and uniqueness of the solution for the stochastic variational inequality with oblique subgradients of the following form:{l} dX_{t}+H(X_{t}) \partial \phi (X_{t}) (dt) \ni f(t,X_{t}) dt+g(t,X_{t})…
In this paper, we study the mean reflected stochastic differential equations driven by G-Brownian motion, where the constraint depends on the expectation of the solution rather than on its paths. Well-posedness is achieved by first…
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…
Given a L\'evy process $L$, we consider the so-called statistical Skorohod embedding problem of recovering the distribution of an independent random time $T$ based on i.i.d. sample from $L_{T}.$ Our approach is based on the genuine use of…
We show that a pseudospectral representation of the wavefunction using multiple spatial domains of variable size yields a highly accurate, yet efficient method to solve the time-dependent Schr\"odinger equation. The overall spatial domain…
This paper establishes the well-posedness of stochastic partial differential equations with reflection in an infinite-dimensional ball, within the fully local monotone framework. Our result is very general, including many important models…
We study the well-posedness of a coupled system of Skorohod-like stochastic differential equations with reflecting boundary condition. The setting describes the evacuation dynamics of a mixed crowd composed of both active and passive…