Related papers: Local linear estimator for stochastic differential…
We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…
We study a one-dimensional kinetic stochastic model driven by a L{\'e}vy process with a non-linear time-inhomogeneous drift. More precisely, the process $(V,X)$ is considered, where $X$ is the position of the particle and its velocity $V$…
We discuss nonparametric estimation of linear multiplier in a trend coefficient in models governed by an $\alpha$-stable small noise.
We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…
In this paper we present an estimator for the three-dimensional parameter $(\sigma, \alpha, H)$ of the linear fractional stable motion, where $H$ represents the self-similarity parameter, and $(\sigma, \alpha)$ are the scaling and stability…
In this paper we prove a derivative formula of Bismut-Elworthy-Li's type as well as gradient estimate for stochastic differential equations driven by $\alpha$-stable noises, where $\alpha\in(0,2)$. As an application, the strong Feller…
Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast…
We investigate the parameter estimation and prediction of two forms of the stochastic SIR model driven by small L\'{e}vy noise with time-dependent periodic transmission. We present consistency and rate of convergence results for the…
Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…
For a L\'evy basis $L$ on $\mathbb{R}^d$ and a suitable kernel function $f:\mathbb{R}^d \to \mathbb{R}$, consider the continuous spatial moving average field $X=(X_t)_{t\in \mathbb{R}^d}$ defined by $X_t = \int_{\mathbb{R}^d} f(t-s) \,…
In this paper we develop an $L_2$-theory for stochastic partial differential equations driven by L\'evy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of…
We address estimation of parametric coefficients of a pure-jump L\'evy driven univariate stochastic differential equation (SDE) model, which is observed at high frequency over a fixed time period. It is known from the previous study Masuda…
In this paper we study the convergence of solutions for (possibly degenerate) stochastic differential equations driven by L\'evy processes, when the coefficients converge in some appropriate sense. First, we prove, by means of a…
We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive L\'{e}vy noise. The main result is applicable to various types of…
We study the effective reduction for a nonlocal stochastic partial differential equation with oscillating coefficients. The nonlocal operator in this stochastic partial differential equation is the generator of non-Gaussian L\'{e}vy…
This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by L\'evy noise, particularly when the sample paths are sparse. Specifically, given $n$…
This paper studies the weak convergence order of the stochastic theta method for stochastic differential equations (SDEs) driven by time-changed L\'{e}vy noise under global Lipschitz and linear growth conditions. In contrast to classical…
We establish asymptotic properties of $M$-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, $\theta$-weak dependence,…
We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter epsilon greater than zero. The estimator, based…
We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest…