We describe a method of approximation of strong solutions to Stratonovich differential equations, that depends only on the Brownian motion defining the equation. h being the step size, it is known that the order of convergence of such approximations is h in the general case, and of h in some...

We propose a method for the simultaneous estimation of the drift and diffusion coefficients of stochastic differential equations (SDE) from panel data. The method involves matching the distribution of the experimental/field data with a panel of simulated data generated by a Monte Carlo...

We apply a new simulation scheme proposed by Kusuoka to finance problems. By using this method, we achieve 6500 times faster simulation than traditional Euler–Maruyama scheme.

The main discretization schemes for diffusion processes, both unrestricted and reflecting in a hyper-rectangle, are considered. For every discretized path, an `antithetic' path is obtained by changing the sign of the driving random variables, which are chosen symmetric. It is shown that, under...

In this paper we consider the simulation of probabilistic chemical reactions in isothermal and adiabatic conditions. Models for reactions under isothermal conditions result in advection equations, adiabatic conditions yield the reactive Euler equations. In order to treat with scattering data,...

In this article we discuss the estimation of continuous time interest rate models driven by fractional Brownian motion (fBm) using discretely sampled data. In the presence of a fractional Brownian motion, usual estimation methods for continuous time models are not appropriate since in general...

Let Xt, t ∈ [0,T], be the solution of a stochastic differential equation, and let Xth, t ∈ [0,T], be the Euler approximation with the step h = Tn. It is known that, for a wide class of functions f, the error Ef(XTh) − Ef(XT) is O(h) or, more exactly, C · h + O(h2). We propose an extension...

In this article we compare the mean-square stability properties of the θ-Maruyama and θ-Milstein method that are used to solve stochastic differential equations. For the linear stability analysis, we propose an extension of the standard geometric Brownian motion as a test equation and consider...