Related papers: Strong Convergence Rates for Cox-Ingersoll-Ross Pr…

We study convergence properties of the full truncation Euler scheme for the Cox-Ingersoll-Ross process in the regime where the boundary point zero is inaccessible. Under some conditions on the model parameters (precisely, when the Feller…

Cox-Ingersoll-Ross (CIR) processes are widely used in financial modeling such as in the Heston model for the approximative pricing of financial derivatives. Moreover, CIR processes are mathematically interesting due to the irregular square…

We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we prove a uniform moment bound and strong error results of order…

In this paper, we investigate the optimal strong convergence rate of numerical approximations for the Cox--Ingersoll--Ross model driven by fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. To deal with the difficulties caused…

Cox-Ingersoll-Ross (CIR) processes are extensively used in state-of-the-art models for the approximative pricing of financial derivatives. In particular, CIR processes are day after day employed to model instantaneous variances (squared…

We introduce a semi-implicit Milstein approximation scheme for some class of non-colliding particle systems modeled by systems of stochastic differential equations with non-constant diffusion coefficients. We show that the scheme converges…

We present new high order approximations schemes for the Cox-Ingersoll-Ross (CIR) process that are obtained by using a recent technique developed by Alfonsi and Bally (2021) for the approximation of semigroups. The idea consists in using a…

We establish quantitative convergence rates for stochastic particle approximation based on Nanbu-type Monte Carlo schemes applied to a broad class of collisional kinetic models. Using coupling techniques and stability estimates in the…

In this paper we study the rate of convergence of a symmetrized version of the Milstein scheme applied to the solution of the one dimensional SDE $$X_t = x_0 + \int_{0}^t{b(X_s)ds}+\int_{0}^t{\sigma |X_s|^\alpha dW_s}, \;x_0>0,\;\sigma>0,\;…

In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Poisson point process. We show that the so-called Kantorovich-Rubinstein distance between such a…

For a class of (non-symmetric) diffusion processes on a length space, which in particular include the (reflecting) diffusion processes on a connected compact Riemannian manifold, the exact convergence rate is derived for $({\mathbb E}…

In this paper, we quantify the rate of convergence between the distribution of number of zeros of random trigonometric polynomials (RTP) with i.i.d. centered random coefficients and the number of zeros of a stationary centered Gaussian…

We investigate the long-time asymptotic behavior of various entropy measures associated with the Cox-Ingersoll-Ross (CIR) and squared Bessel processes. As the one-dimensional distributions of both processes follow noncentral chi-squared…

Inspired by the truncated Euler-Maruyama method developed in Mao (J. Comput. Appl. Math. 2015), we propose the truncated Milstein method in this paper. The strong convergence rate is proved to be close to 1 for a class of highly non-linear…

In this paper we derive a new direct inversion method to simulate squared Bessel processes. Since the transition probability of these processes can be represented by a non-central chi-square distribution, we construct an efficient and…

This paper establishes quantitative limit theorems for two classes of Cox point processes, quantifying their convergence to a Poisson point process (PPP). We employ Stein's method for PPP aproximation, leveraging the generator approach and…

In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…

A new class of explicit Milstein schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that…

We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…

The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square density based on sums of powers of generalized Gaussian random…