Related papers: Uniqueness for stochastic differential equations i…

We consider non-degenerate SDEs with a $\beta$-Holder continuous and bounded drift term and driven by a Levy noise $L$ which is of $\alpha$-stable type. If $\alpha \in [1,2)$ and $\beta \in (1 - \frac{\alpha}{2},1) $ we show pathwise…

We prove path-by-path uniqueness of solution to hyperbolic stochastic partial differential equations when the drift coefficient is the difference of two componentwise monotone Borel measurable functions of spatial linear growth. The…

It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to…

Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a…

In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [2] by using Dirichlet form theory. By this definition, we can consider the stochastic reflection…

Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the unique strong solvability of time-inhomogeneous stochastic differential equations with drift coefficients in critical Lebesgue spaces,…

We consider a one-dimensional stochastic differential equations (SDE) with irregular coefficients. The purpose of this paper is to estimate the $L^p(\Omega)$-difference of SDEs using the norm of the difference of coefficients, where the…

The Swift-Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of pattern formation. Following a recent study by Bramburger…

We prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework of stochastic evolution equations and the method of vanishing…

We emphasize that for a stochastic differential equation with isotropic stable additive noise and non Lipschitz drift, when considering an appropriate discretization scheme and the associated weak error, it is somehow natural to consider a…

Uniqueness of positive solutions to viscous Hamilton-Jacobi-Bellman (HJB) equations of the form $-\Delta u(x) + \frac{1}{\gamma} |D{u}(x)|^\gamma = f(x) - \lambda$, with $f$ a coercive function and $\lambda$ a constant, in the subquadratic…

We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…

We establish weak existence and uniqueness for random field solutions of the one-dimensional SPDE \[ d_tX_t = \frac{1}{2}\Delta X_t +h(X_t)+ \sqrt{X_t}\dot{W}, \quad t\geq 0,\] where $\dot{W}$ is space-time white noise and $h$ is a bounded…

We extend Krylov and R\"{o}ckner's result \cite{KR} to the drift coefficients in critical Lebesgue space, and prove the existence and uniqueness of weak solutions for a class of SDEs. To be more precise, let $b: [0,T]\times{\mathbb…

For continuous \gamma, g:[0,1]\to(0,\infty), consider the degenerate stochastic differential equation dX_t=[1-|X_t|^2]^{1/2}\gamma(|X_t|) dB_t-g(|X_t|)X_t dt in the closed unit ball of R^n. We introduce a new idea to show pathwise…

We prove $L^{p}$-uniqueness of Dirichlet operators for Gibbs measures on the path space $C(\mathbb R, \mathbb R^{d})$ associated with exponential type interactions in infinite volume by extending an SPDE approach presented in previous work…

A new explicit stochastic scheme of order 1 is proposed for solving commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The proposed method is a semi-tamed version of Milstein scheme to…

This paper develops an $\alpha$-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed L\'evy noise (TCSDEwLNs) with time-space-dependent…

We study path-dependent SDEs in Hilbert spaces. By using methods based on contractions in Banach spaces, we prove existence and uniqueness of mild solutions, continuity of mild solutions with respect to perturbations of all the data of the…

We introduce an explicit adaptive Milstein method for stochastic differential equations (SDEs) with no commutativity condition. The drift and diffusion are separately locally Lipschitz and together satisfy a monotone condition. This method…