In this paper we propose a Bayesian method for estimating hyperbolic diffusion models. The approach is based on the Markov Chain Monte Carlo (MCMC) method after discretization via the Milstein scheme. Our simulation study shows that the hyperbolic diffusion exhibits many of the stylized facts about asset returns documented in the financial econometrics literature, such as a slowly declining aut...

Velocities and Brownian effects at nanoscales near channel walls can be measured experimentally in an image plane parallel to the wall by evanescent wave illumination techniques [R. Sadr, M. Yoda, Z. Zheng, and A. T. Conlisk, J. Fluid Mech., 506 (2004), pp. 357–367], but the depth of field in this technique is difficult to modify. Assuming mobility of spherical particles dominated by hydrodynam...

A new algorithm for simulating stochastic partial differential equations (SPDEs) of evolutionary type, which is in some sense an infinite dimensional analog of Milstein’s scheme for finite dimensional stochastic ordinary differential equations (SODEs), is introduced and analyzed in this article. The Milstein scheme is known to be impressively efficient for scalar one-dimensional SODEs but only ...

Abstract We introduce an explicit adaptive Milstein method for stochastic differential equations with no commutativity condition. The drift and diffusion are separately locally Lipschitz together satisfy a monotone This relies on class of path-bounded time-stepping strategies which work by reducing the stepsize as solutions approach boundary sphere, invoking backstop in event that timestep beco...

in this paper, a class of semi-implicit two-stage stochastic runge-kutta methods (srks) of strong global order one, with minimum principal error constants are given. these methods are applied to solve itô stochastic differential equations (sdes) with a wiener process. the efficiency of this method with respect to explicit two-stage itô runge-kutta methods (irks), it method, milstien method, sem...

Optimal as well as recursive parameter estimation for semimartingales had been studied in Thavaneswaran and Thompson [1, 2]. Recently, there has been a growing interest in modeling volatility of the observed process by nonlinear stochastic processes (Taylor [3]). In this paper, we study the recursive estimates for various classes of discretely sampled continuous time stochastic volatility model...

Thomas Eng, A. Chockalingam, Member, IEEE, and Laurence B. Milstein, Fellow, IEEE Abstract— The effect of phase noise on the capacities of coherently demodulated hybrid FDMA/CDMA systems operating over a multipath Rayleigh fading channel is investigated. Using an approximate upper bound on the BER performance which has been derived and presented in a previous paper, the capacities of the FDMA/C...

Last week we reviewed the 1984 Nobel laureates in medicine: immunologists Niels K. Jerne, Georges J.F. Kohler, and C6sar Milstein. 1 In this week’s essay the prizewinners in physics and chemistry are discussed. The 1984 physics prize was shared by Carlo Rubbia, Harvard University and the European Center for Nuclear Research (CERN), Geneva, Switzerland, and Simon van der Meer, also of CERN. The ...