Related papers: On the one-sided Tanaka equation with drift
We study the existence and uniqueness, the regularity, and the long-time behavior of strong solutions to stochastic curve shortening flow driven by a transport-type pure jump L\'evy noise. To obtain the existence and uniqueness of strong…
In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison…
In this paper, we are interested in the following one dimensional forward stochastic differential equation (SDE) \[ d X_{t}=b(t,X_{t},\omega)d t +\sigma d B_{t},\quad 0\leq t\leq T,\quad X_{0}=\,x\in \mathbb{R}, \] where the driving noise…
In this paper, we establish strong backward uniqueness for solutions to sublinear parabolic equations of the type (1.1). The proof of our main result Theorem 1.1 is achieved by means of a new Carleman estimate and a Weiss type monotonicity…
Existence, uniqueness, and regularity of time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space are investigated. We consider the Navier-Stokes equations with a non-zero drift term corresponding to the…
We prove the existence and weak uniqueness of weak solutions of It\^o's stochastic time dependent equations with irregular diffusion and drift terms of Morrey class with mixed norms.
The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained. The proofs are based…
In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of the adapted solution, either when the terminal value and the…
We study a large class of McKean-Vlasov SDEs with drift and diffusion coefficient depending on the density of the solution's time marginal laws in a Nemytskii-type of way. A McKean-Vlasov SDE of this kind arises from the study of the…
We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a new method that maps the problem of computing the persistence to the problem of finding the…
We prove the existence and uniqueness of a strong solution for an SDE on a semi-axis with singularities at the point 0. The result obtained yields, for example, the strong uniqueness of non-negative solutions to SDEs governing Bessel…
In this article we consider a class of nonlinear integro-differential equations of the form $$\inf_{\tau \in\mathcal{T}} \bigg\{\int_{\mathbb{R}^d} (u(x+y)+u(x-y)-2u(x))\frac{k_{\tau}(x,y)}{|y|^{d+2s}} \,dy+ b_{\tau}(x) \cdot \nabla…
In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of…
In this paper, we give the existence and uniqueness of the strong solution of one dimensional linear parabolic equation with mixed boundary conditions. The boundary conditions can be any kind of mixed Dirichlet, Neumann and Robin boundary…
We study existence and uniqueness for one-dimensional generalized stochastic differential equations with singular coefficients, including distributional drift and degenerate, possibly discontinuous, diffusion coefficients. Such…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
This paper is concerned with the stochastic Hamilton-Jacobi-Bellman equation with controlled leading coefficients, which is a type of fully nonlinear backward stochastic partial differential equation (BSPDE for short). In order to formulate…
We study a two-dimensional stochastic differential equation that has a unique weak solution but no strong solution. We show that this SDE shares notable properties with Tsirelson's example of a one-dimensional SDE with no strong solution.…
We study the stability of solution branches for the Lichnerowicz-York equation at moment of time symmetry with constant unscaled energy density. We prove that the weak-field lower branch of solutions is stable whilst the upper branch of…
We prove that joint uniqueness in law and the existence of a strong solution imply pathwise uniqueness for variational solutions to stochastic partial differential equations of the form \begin{align*}…