相关论文: Convergence of multi-dimensional quantized $SDE$'s

In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the…

We examine the relation between a stochastic version of the rough path integral with the symmetric-Stratonovich integral in the sense of regularization. Under mild regularity conditions in the sense of Malliavin calculus, we establish…

We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observations of the driving Brownian motion. We prove lower error…

In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated. In particular, equations are studied that cover the linear…

In this paper, we establish the strong well-posedness of SDEs with merely integrable time-dependent drifts driven by fractional Brownian motions with Hurst parameter H<1/2. Our result holds over the entire subcritical regime and can be…

This paper develops an It\^o-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters \( H \in (\frac{1}{3}, \frac{1}{2}] \), using the Lyons' rough path framework. This approach is designed to fill…

In this paper, we are interested in path-dependent stochastic differential equations (SDEs) which are controlled by Brownian motion and its delays. Within this non-Markovian context, we give a H \"ormander-type criterion for the regularity…

Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…

In this work, we present a detailed analysis on the exact expression of the $L^2$-norm of the symmetric-Stratonovich stochastic integral driven by a multi-dimensional fractional Brownian motion $B$ with parameter $\frac{1}{4} < H <…

We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…

In a recent paper (arXiv:1501.06164) the author has introduced a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows the interpretation of merely measurable maps as solutions. This…

This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…

We study It\^o SDE systems driven by oscillating functions of a single It\^o diffusion process. In the limit when oscillations become fast, we show that the solution process converges in law to the process defined by an SDE system driven by…

We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are obtained by obtained by computing a directional derivative of the weak…

In a previous work, we have defined a Tanaka SDE related to Walsh Brownian motion which depends on kernels. It was shown that there are only one Wiener solution and only one flow of mappings solving this equation. In the terminology of Le…

In this thesis, we extend the recently introduced theory of stochastic modified equations (SMEs) for stochastic gradient optimization algorithms. In Ch. 3 we study time-inhomogeneous SDEs driven by Brownian motion. For certain SDEs we prove…

The dynamic formulation of optimal transport has attracted growing interests in scientific computing and machine learning, and its computation requires to solve a PDE-constrained optimization problem. The classical Eulerian discretization…

Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…

We investigate the stability of traveling-pulse solutions to the stochastic FitzHughNagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable fast traveling…

In this article we investigate the numerical solution of a scalar semilinear stochastic delay differential equation (SDDE) where the linear instantaneous feedback and nonlinear delayed feedback terms are perturbed by a pair of standard…