Related papers: Explicit positivity preserving numerical method fo…
An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A…
We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition…
In this paper, we analyze the drift-implicit (or backward) Euler numerical scheme for a class of stochastic differential equations with unbounded drift driven by an arbitrary $\lambda$-H\"older continuous process, $\lambda\in(0,1)$. We…
We study the strong rate of convergence of the Euler--Maruyama scheme for a multidimensional stochastic differential equation (SDE) $$ dX_t = b(X_t) \, dt + dL_t, $$ with irregular $\beta$-H\"older drift, $\beta > 0$, driven by a L\'evy…
In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor-corrector Euler-Maruyama methods is designed…
In this paper the numerical approximation of stochastic differential equations satisfying a global monotonicity condition is studied. The strong rate of convergence with respect to the mean square norm is determined to be $\frac{1}{2}$ for…
Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that…
We study the strong convergence order of the Euler-Maruyama scheme for scalar stochastic differential equations with additive noise and irregular drift. We provide a general framework for the error analysis by reducing it to a weighted…
This paper develops a family of fast, structure-preserving numerical algorithms for the nonlinear Maxwell-Ampere Nernst-Planck equations. For the first-order scheme, the Slotboom transformation rewrites the Nernst-Planck equation to enable…
We study the stochastic Leray-{\alpha} model of Euler equations with transport noise. We first use weak convergence approach to show the large deviations of the stochastic Leray-{\alpha} model of Euler equations in a suitable scaling limit.…
This article present a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade. One multiplicatively…
We present and analyze finite difference numerical schemes for the Allen Cahn/Cahn-Hilliard equation with a logarithmic Flory Huggins energy potential. Both the first order and second order accurate temporal algorithms are considered. In…
For $\alpha\in (0,1)$, we consider stochastic differential equations driven by one-sided stable processes of order $\alpha$: \[dX_t= \phi(X_{t-})\ dZ_t.\] We prove that pathwise uniqueness holds for this equation under the assumptions that…
This paper establishes a discretization scheme for a large class of stochastic differential equations driven by a time-changed Brownian motion with drift, where the time change is given by a general inverse subordinator. The scheme involves…
In this paper we propose an explicit and positivity preserving scheme for the mean reverting CEV model which converges in the mean square sense with convergence order $a(a-1/2)$.
We propose two Euler-Maruyama (EM) type numerical schemes in order to approximate the invariant measure of a stochastic differential equation (SDE) driven by an $\alpha$-stable L\'evy process ($1<\alpha<2$): an approximation scheme with the…
Stable distributions are a celebrated class of probability laws used in various fields. The $\alpha$-stable process, and its exponentially tempered counterpart, the Classical Tempered Stable (CTS) process, are also prominent examples of…
In this paper, we are interested in constructing a scheme solving compressible Navier--Stokes equations, with desired properties including high order spatial accuracy, conservation, and positivity-preserving of density and internal energy…
This paper focuses on the numerical scheme for multiple-delay stochastic differential equations with partially H\"older continuous drifts and locally H\"older continuous diffusion coefficients. To handle with the superlinear terms in…
In this paper, we examine the performance of randomised Euler-Maruyama (EM) method for additive time-inhomogeneous SDEs with an irregular drift driven by symmetric $\alpha$-table process, $\alpha\in (1,2)$. In particular, the drift is…