Related papers: C\`adl\`ag Rough Differential Equations with Refle…

A theory of differential equations driven by a non-differentiable path has recently been developed by Lyons. We develop an alternative approach to this theory, using (modified Euler approximations), and investigate its applicability to…

We study reflected solutions of one-dimensional backward doubly stochastic differential equations (BDSDEs in short). The "reflected" keeps the solution above a given stochastic process. We get the uniqueness and existence by penalization.…

When the one-form is $Lip\left(\gamma-1\right) $ with $\gamma >p\geq 1$, we construct the integral of a branched $p$-rough path, which defines another branched $p$-rough path. We derive a quantitative bound for this integral and prove that…

Radiative backpropagation-based (RB) methods efficiently compute reverse-mode derivatives in physically-based differentiable rendering by simulating the propagation of differential radiance. A key assumption is that differential radiance is…

We study a large class of stochastic $p$-Laplace Allen-Cahn equations with singular potential. Under suitable assumptions on the (multiplicative-type) noise we first prove existence, uniqueness, and regularity of variational solutions.…

Although Neural Differential Equations have shown promise on toy problems such as MNIST, they have yet to be successfully applied to more challenging tasks. Inspired by variational methods for image restoration relying on partial…

We prove a uniqueness result for the broken ray transform acting on the sums of functions and $1$-forms on surfaces in the presence of an external force and a reflecting obstacle. We assume that the considered twisted geodesic flows have…

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution…

We study the tunneling through an arbitrary number of finite rectangular opaque barriers and generalize earlier results by showing that the total tunneling phase time depends neither on the barrier thickness nor on the inter-barrier…

Recently it was proved that the group of rough paths modulo tree-like equivalence is isomorphic to the corresponding signature group through the signature map S (a generalized notion of taking iterated path integrals). However, the proof of…

We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a…

Using a recently developed procedure - multiple wave packet decomposition - here we study the phase time formulation for tunneling/reflecting particles colliding with a potential barrier. To partially overcome the analytical difficulties…

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…

We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we…

This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is…

Let v be a bounded function with bounded support in R^d, d>=3. Let x,y in R^d. Let Z(t) denote the path integral of v along the path of a Brownian bridge in R^d which runs for time t, starting at x and ending at y. As t->infty, it is…

This article focuses on parabolic equations with rough diffusion coefficients which are ill-posed in the classical sense of distributions due to the presence of a singular forcing. Inspired by the philosophy of rough paths and regularity…

In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator $f$ has quadratic growth in the $z$-variable. In…

Complex quantum trajectory approach, which arose from a modified de Broglie-Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft…

We prove existence and uniqueness of the reflected backward stochastic differential equation's (RBSDE) solution with a lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous in a filtration…