相关论文: Instabilities of Super-Time-Stepping Methods on th…

We reconcile rough volatility models and jump models using a class of reversionary Heston models with fast mean reversions and large vol-of-vols. Starting from hyper-rough Heston models with a Hurst index $H \in (-1/2,1/2)$, we derive a…

The residual-based variational multiscale (VMS) formulation has achieved remarkable success in large-eddy simulation of turbulent flows. However, its temporal discretization has largely remained limited to second-order implicit schemes. The…

The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe…

In [Baeza et al., Computers and Fluids, 159, 156--166 (2017)] a new method for the numerical solution of ODEs is presented. This methods can be regarded as an approximate formulation of the Taylor methods and it follows an approach that has…

We address the stabilization of both classical and quantum systems modeled by jump-diffusion stochastic differential equations using a novel hysteresis switching strategy. Unlike traditional methods that depend on global Lyapunov functions…

We present fifth order Runge-Kutta-Nystr\"om methods, where we allow the timestep coefficients to assume complex values. Among the methods with complex timesteps, we focus on the ones with the coefficients that have positive real parts.…

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large…

This paper pursues a two-fold goal. Firstly, we aim to derive novel second-order characterizations of important robust stability properties of perturbed Karush-Kuhn-Tucker systems for a broadclass of constrained optimization problems…

This paper investigates the asymptotic behavior of suitably time-modulated Hawkes processes with heavy-tailed kernels in a nearly unstable regime. We show that, under appropriate scaling, both the intensity processes and the rescaled Hawkes…

When a high dimension system of ordinary differential equations is solved numerically, the computer memory capacity may be compromised. Thus, for such systems, it is important to incorporate low memory usage to some other properties of the…

We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…

This paper studies set-invariance and stabilization of hyperbolic sets over rate-limited channels for discrete-time control systems. We first investigate structural and control-theoretic properties of hyperbolic sets, in particular such…

We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…

Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…

We undertake a systematic exploration of recurrent patterns in a 1-dimensional Kuramoto-Sivashinsky system. For a small, but already rather turbulent system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set…

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible…

We study, analytically and numerically, the stability of quantum motion for a classically chaotic system. We show the existence of different regimes of fidelity decay which deviate from Fermi Golden rule and Lyapunov decay.

The theoretical justification of the Hybrid Monte Carlo algorithm depends upon the molecular dynamics trajectories within it being exactly reversible. If computations were carried out with exact arithmetic then it would be easy to ensure…

We study stability issue of reset and impulsive switched systems. We find time constraints (dwell time and flee time) on switching signals which stabilize a given reset switched system. For a given collection of matrices, we find an…

An analytical formula for the probability distribution of stock-market returns, derived from the Heston model assuming a mean-reverting stochastic volatility, was recently proposed by Dragulescu and Yakovenko in Quantitative Finance 2002.…