Related papers: Stochastic invariance in infinite dimension beyond…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
We prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a stochastic partial differential equation driven by a finite dimensional Wiener process. The equation is formulated in a semi-abstract form…
We study hypoelliptic stochastic differential equations (SDEs) and their connection to degenerate-elliptic boundary value problems on bounded or unbounded domains. In particular, we provide probabilistic conditions that guarantee that the…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
We establish an invariance principle corresponding to the universality of random matrices. More precisely, we prove the dynamical universality of random matrices in the sense that, if the random point fields $ \muN $ of $ \nN $-particle…
One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our…
We consider a diffusion process in $\mathbb{R}^d$ with a generator of the form $ L:=\frac 12 e^{V(x)}div(e^{-V(x)}\nabla ) $ where $V$ is measurable and periodic. We only assume that $e^V$ and $e^{-V}$ are locally integrable. We then show…
We consider stochastic semilinear partial differential equations with Lipschitz nonlinear terms. We prove existence and uniqueness of an invariant measure and the existence of a solution for the corresponding Kolmogorov equation in the…
Existence, uniqueness, and regularity of a strong solution are obtained for stochastic PDEs with a colored noise $F$ and its super-linear diffusion coefficient: $$ du=(a^{ij}u_{x^ix^j}+b^iu_{x^i}+cu)dt+\xi|u|^{1+\lambda}dF, \quad…
Sampling viable 3D structures (e.g., molecules and point clouds) with SE(3)-invariance using diffusion-based models proved promising in a variety of real-world applications, wherein SE(3)-invariant properties can be naturally characterized…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
The object of the present paper is to find new sufficient conditions for the existence of unique strong solutions to a class of (time-inhomogeneous) stochastic differential equations with random, non-Lipschitzian coefficients. We give an…
This paper establishes a Freidlin-Wentzell large deviation principle for stochastic differential equations(SDEs) under locally weak monotonicity conditions and Lyapunov conditions. We illustrate the main result of the paper by showing that…
We consider an infinite dimensional diffusion on $T^{\mathbb Z^d}$, where $T$ is the circle, defined by an infinitesimal generator of the form $L=\sum_{i\in\mathbb Z^d}\left(\frac{a_i(\eta)}{2}\partial^2_i +b_i(\eta)\partial_i\right)$, with…
In this paper, we develop numerical methods for solving Stochastic Differential Equations (SDEs) with solutions that evolve within a hypercube $D$ in $\mathbb{R}^d$. Our approach is based on a convex combination of two numerical flows, both…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
This paper is concerned with stochastic systems whose state is a diffusion process governed by an Ito stochastic differential equation (SDE). In the framework of a nominal white-noise model, the SDE is driven by a standard Wiener process.…
We consider certain random matrix eigenvalue dynamics, akin to Dyson Brownian motion, introduced by Rider and Valko. We show that from every initial condition, including ones involving coinciding coordinates, the dynamics, enhanced with…
In this paper, we discuss the approximate controllability for control systems governed by stochastic evolution hemivariational inequalities in Hilbert spaces. The interest in studying this type of equation comes from its application in some…