Related papers: Optimal simulation schemes for L\'evy driven stoch…
We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond.…
Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…
The problem of the construction of strong approximations with a given order of convergence for jump-diffusion equations is studied. General approximation schemes are constructed for L\'evy type stochastic differential equation. In…
We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general L\'evy…
In this paper, we get some convergence rates in total variation distance in approximating discretized paths of L{\'e}vy driven stochastic differential equations, assuming that the driving process is locally stable. The particular case of…
In this paper, we study the asymptotic behavior for multi-scale stochastic differential equations driven by L\'evy processes. The optimal strong convergence order 1/2 is obtained by studying the regularity estimates for the solution of…
We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a L\'evy process. Our results are valid for a large…
We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is when the limiting equation admits both a…
We develop a computational method for expected functionals of the drawdown and its duration in exponential L\'evy models. It is based on a novel simulation algorithm for the joint law of the state, supremum and time the supremum is attained…
We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally…
It is well known that for a stochastic differential equation driven by L\'evy noise, the temporal H\"older continuity in $L^p$ sense of the exact solution does not exceed $1/p$. This leads to that the $L^p$-strong convergence order of a…
In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions…
Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…
In this work, we present a general Milstein-type scheme for McKean-Vlasov stochastic differential equations (SDEs) driven by Brownian motion and Poisson random measure and the associated system of interacting particles where drift,…
We consider the explicit numerical approximations of stochastic differential equations (SDEs) driven by Brownian process and Poisson jump. It is well known that under non-global Lipschitz condition, Euler Explicit method fails to converge…
This paper considers the problem of partially observed optimal control for forward stochastic systems which are driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
In this paper, we study the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by a additive fractional Brownian motion (fBm) with Hurst parameter $H>\frac 12$ and Poisson…
We consider a generic and explicit tamed Euler--Maruyama scheme for multidimensional time-inhomogeneous stochastic differential equations with multiplicative Brownian noise. The diffusive coefficient is uniformly elliptic, H\"older…
The aim of this work is to provide the strong convergence results of numerical approximations of a general second order non-autonomous semilinear stochastic partial differential equation (SPDE) driven simultaneously by an additive…