The SIR infections disease model is an important biologic model. In this paper, the split-step forward Milstein method, is used for solving numerically stochastic SIR model. The stability of this method is better than the Milsteins methods.

Stability analysis of numerical methods for ordinary differential equations (ODEs) is motivated by the question “for what choices of stepsize does the numerical method reproduce the characteristics of the test equation?” We study a linear test equation with a multiplicative noise term, and consider mean-square and asymptotic stability of a stochastic version of the theta method. We extend some ...

Stability analysis of numerical methods for ordinary diierential equations is motivated by the question \for what choices of stepsize does the numerical method reproduce the characteristics of the test equation?" We study a linear test equation with a multiplicative noise term, and consider mean-square and asymptotic stability of a stochastic version of the Theta Method. We extend some mean-squ...

Network simulation models are becoming common for modeling the spread of infections. However, speed is often an issue for large populations. Choosing a discrete time simulation (DTS) over a discrete event simulation (DES) helps to remedy this problem at the cost some accuracy. We analyze and quantify the loss in accuracy for the common SI and SIS processes. Specifically we prove the DTS method ...

Good morning Chairman Conyers, Ranking Member Smith, and Members of the Committee. Thank you for inviting me to speak today. My name is Christopher J. Mayer. I am the Paul Milstein Professor of Real Estate and Senior Vice Dean at Columbia Business School. I have spent the last 16 years studying housing markets and credit while working at the Federal Reserve Bank of Boston and serving on the fac...

The Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential equations with a strong order of convergence one. The scheme has been extended to the stochastic delay differential equations but the analysis of the convergence is technically complicated due to anticipative integrals in the remainder terms. This paper employs an elementary method to derive the Milstein...

Abstract. This paper focuses on two variants of the Milstein scheme, namely the split-step backward Milstein method and a newly proposed projected Milstein scheme, applied to stochastic differential equations which satisfy a global monotonicity condition. In particular, our assumptions include equations with super-linearly growing drift and diffusion coefficient functions and we show that both ...

A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semimartingales. A necessary and sufficient condition was provided for this rate to be 1/n when the SDE is driven by a vector of continuous local martingales, or continuous semimartingales under an additional assumptio...

E|Bt −Bs| = cp|t− s| , s, t ∈ [0, 1], with cp = E(|G|), G ∼ N (0, 1), and, consequently, almost all sample paths of B are Hölder continuous of any order α ∈ (0,H). The study of stochastic differential equations driven by B has been considered by using several methods. For instance, in [22] one uses fractional calculus of same type as in [25]; in [2] one uses rough paths theory introduced in [11...