Related papers: Pathwise uniqueness for two dimensional reflecting…

We prove the existence and uniqueness of a strong solution of a stochastic differential equation with normal reflection representing the random motion of finitely many globules. Each globule is a sphere with time-dependent random radius and…

We investigate a stochastic transport equation driven by a multiplicative noise. For $L^q(0,T;W^{1,p}({\mathbb R}^d;{\mathbb R}^d))$ drift coefficient and $W^{1,r}({\mathbb R}^d)$ initial data, we obtain the existence and uniqueness of…

Recently, domain-uniform stabilizability and detectability has been the central assumption %in order robustness results on the to ensure robustness in the sense of exponential decay of spatially localized perturbations in optimally…

It is proved that, in two dimensions, the Calder\'on inverse conductivity problem in Lipschitz domains is stable in the $L^p$ sense when the conductivities are uniformly bounded in any fractional Sobolev space $W^{\alpha,p}$ $\alpha>0,…

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of…

The signature of Brownian motion in $\mathbb{R}^{d}$ over a running time interval $[0,T]$ is the collection of all iterated Stratonovich path integrals along the Brownian motion. We show that, in dimension $d\geq 2$, almost all Brownian…

Using one-dimensional branching Brownian motion in a periodic environment, we give probabilistic proofs of the asymptotics and uniqueness of pulsating travelling waves of the F-KPP equation in a periodic environment. This paper is a sequel…

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…

We present a self-contained proof of the reflection principle for Brownian Motion.

It is well-known that a stochastic differential equation (sde) on a Euclidean space driven by a (possibly infinite-dimensional) Brownian motion with Lipschitz coefficients generates a stochastic flow of homeomorphisms. If the Lipschitz…

We prove the triviality of the first L2 cohomology class of based path spaces of Riemannian manifolds furnished with Brownian motion measure, and the consequent vanishing of L2 harmonic one-forms. We give explicit formulae for closed and…

We consider a continuous-time random walk in the quarter plane for which the transition intensities are constant on each of the four faces $(0,\infty)^2$, $F_1=\{0\}\times(0,\infty)$, $F_2=(0,\infty)\times\{0\}$ and $\{(0,0)\}$. We show…

Let $D$ be an unbounded domain in $\RR^d$ with $d\geq 3$. We show that if $D$ contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on $\overline D$ is transient. Next assume that RBM $X$ on $\overline D$…

The article presents results on existence and uniqueness of mild solutions to a class of non linear neutral stochastic functional differential equations (NSFDEs) driven by Fractional Brownian motion in a Hilbert space with non-Lipschitzian…

We study strong existence and pathwise uniqueness for a class of infinite-dimensional singular stochastic differential equations (SDE), with state space as the cone $\{x \in \mathbb{R}^{\mathbb{N}}: -\infty < x_1 \leq x_2 \leq \cdots\}$,…

We prove uniqueness for Calder\'on's problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three and four dimensional cases, this confirms a conjecture of Uhlmann. Our proof…

In this paper, we study the uniqueness and existence of solutions of RGSDEs with nonlinear resistance under an integral-Lipschitz condition of coefficients. Moreover we obtain the comparison theorem for RGSDEs with nonlinear resistance.

In this article we prove path-by-path uniqueness in the sense of Davie \cite{Davie07} and Shaposhnikov \cite{Shaposhnikov16} for SDE's driven by a fractional Brownian motion with a Hurst parameter $H\in(0,\frac{1}{2})$, uniformly in the…

Consider the $\lambda$-Green function and the $\lambda$-Poisson kernel of a Lipschitz domain $U\subset \mathbb H^n=\left\{x\in\mathbb R^n:x_n>0\right\}$ for hyperbolic Brownian motion with drift. We provide several relationships that…

In a noise driving by a multivariate point process $\mu$ with predictable compensator $\nu$, we prove existence and uniqueness of the reflected backward stochastic differential equation's solution with a lower obstacle…