A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise

A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter H > 1/2. The estimator is based on discrete time observations of the stochastic differential equation, and using tools from ergodic theory and stochastic analysis we derive its strong consistency.

Parameter estimation for stochastic equations with additive fractional Brownian sheet

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the twoparameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity theory. Mathematics Subject Classification (2000): 60G15, G0H07, 60G35, 62M40

Weak exponential schemes for stochastic differential equations with additive noise

This paper develops weak exponential schemes for the numerical solution of stochastic differential equations (SDEs) with additive noise. In particular, this work provides first and second-order methods which use at each iteration the product of the exponential of the Jacobian of the drift term with a vector. The article also addresses the rate of convergence of the new schemes. Moreover, numeri...

Multilevel Monte Carlo for stochastic differential equations with additive fractional noise

Parameter Estimation in Stochastic Differential Equations

Financial processes as processes in nature, are subject to stochastic fluctuations. Stochastic differential equations turn out to be an advantageous representation of such noisy, real-world problems, and together with their identification, they play an important role in the sectors of finance, but also in physics and biotechnology. These equations, however, are often hard to represent and to re...