Related papers: A note on Asymptotic mean-square stability of stoc…
We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson…
We investigate further qualitative properties of statistically stationary solutions to the Schr\"odinger map equation (SME) and the Binormal Curvature Flow (BCF), continuing the work initiated by E. G., M. Hofmanov\'a. Concerning the…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
In this technical note, we study the mean square stability-based analysis of stochastic continuous-time linear networked systems. The stochastic uncertainty is assumed to enter multiplicatively in system dynamics through input and output…
In this paper, we first establish well-posedness of McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs) with common noise, possibly with coefficients having super-linear growth in the state variable. Second, we present…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients,…
Adaptive time stepping methods for metastable dynamics of the Allen Cahn and Cahn Hilliard equations are investigated in the spatially continuous, semi-discrete setting. We analyse the performance of a number of first and second order…
We address the weak numerical solution of stochastic differential equations driven by independent Brownian motions (SDEs for short). This paper develops a new methodology to design adaptive strategies for determining automatically the…
We propose a semi-discrete scheme for 2D Keller-Segel equations based on a symmetrization reformation, which is equivalent to the convex splitting method and is free of any nonlinear solver. We show that, this new scheme is unconditionally…
We study the effect of fading in the communication channels between sensor nodes on the performance of the incremental least mean square (ILMS) algorithm, and derive steady state performance metrics, including the mean-square deviation…
In this paper we present a complete asymptotic expansion of a symmetric homogeneous stable (balanced), stabilizable and stabilized mean. By including known asymptotic expansions of parametric means it is shown how the obtained coefficients…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
We study stability of so-called synchronous slowly oscillating periodic solutions (SOPSs) for a system of identical delay differential equations (DDEs) with linear decay and nonlinear delayed negative feedback that are coupled through their…
Asynchronous stochastic approximations (SAs) are an important class of model-free algorithms, tools and techniques that are popular in multi-agent and distributed control scenarios. To counter Bellman's curse of dimensionality, such…
In this paper, we propose and analyze a first-order and a second-order time-stepping schemes for the anisotropic phase-field dendritic crystal growth model. The proposed schemes are based on an auxiliary variable approach for the Allen-Cahn…
A scheme for stabilizing stochastic approximation iterates by adaptively scaling the step sizes is proposed and analyzed. This scheme leads to the same limiting differential equation as the original scheme and therefore has the same…
We consider randomized block coordinate stochastic mirror descent (RBSMD) methods for solving high-dimensional stochastic optimization problems with strongly convex objective functions. Our goal is to develop RBSMD schemes that achieve a…
We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples, crude schemes fail to capture the correct limiting…
This paper establishes the asymptotic error distribution of the tamed Euler method for stochastic differential equations (SDEs) with a coupled monotonicity condition, that is, the limit distribution of the corresponding normalized error…