Approximation Of Stochastic Integrals Research Articles

Approximation of stochastic integrals with jumps via weighted BMO approach

Approximation of stochastic integrals with jumps via weighted BMO approach

Stochastic lattice-based modelling of malaria dynamics

BackgroundThe transmission of malaria is highly variable and depends on a range of climatic and anthropogenic factors. In addition, the dispersal of Anopheles mosquitoes is a key determinant that affects the persistence and dynamics of malaria. Simple, lumped-population models of malaria prevalence have been insufficient for predicting the complex responses of malaria to environmental changes.Methods and resultsA stochastic lattice-based model that couples a mosquito dispersal and a susceptible-exposed-infected-recovered epidemics model was developed for predicting the dynamics of malaria in heterogeneous environments. The Ithat{o} approximation of stochastic integrals with respect to Brownian motion was used to derive a model of stochastic differential equations. The results show that stochastic equations that capture uncertainties in the life cycle of mosquitoes and interactions among vectors, parasites, and hosts provide a mechanism for the disruptions of malaria. Finally, model simulations for a case study in the rural area of Kilifi county, Kenya are presented.ConclusionsA stochastic lattice-based integrated malaria model has been developed. The applicability of the model for capturing the climate-driven hydrologic factors and demographic variability on malaria transmission has been demonstrated.

Equivalence of K- and J-methods for limiting real interpolation spaces

We consider limiting real interpolation spaces defined by using powers of iterated logarithms and show their description by means of the J-functional. Our results allow to complement some estimates on approximation of stochastic integrals.

Linear information for approximation of the Itô integrals

We study optimal approximation of stochastic integrals in the Ito sense when linear information, consisting of certain integrals of trajectories of Brownian motion, is available. Upper bounds on the nth minimal error, where n is the fixed cardinality of information, are obtained by the Wagner–Platen algorithm and are O(n − 3/2) or O(n − 2), depending on considered class of integrands. We also show that Ω(n − 2) is a lower bound which holds even for very smooth integrands.

Discrete approximation of stochastic integrals with respect to fractional Brownian motion of Hurst index H>1/2

In this paper we provide a discrete approximation for the stochastic integral with respect to the fractional Brownian motion of Hurst index H>1/2 defined in terms of the divergence operator. To determine the suitable class of integrands for which the approximation holds, we also investigate the relations among the spaces of Malliavin differentiable processes in the fractional and standard case.

On approximation of stochastic integrals with respect to a fractional Brownian motion

There is not abstract.

Approximation of Stochastic Integrals with Applications to Goodness-of-Fit Tests

In this paper stochastic integrals with respect to the basic martingale are approximated by Gaussian processes. The probability inequalities governing this approximation are used to study goodness-of-fit tests based on sublinear functionals of weighted versions of these stochastic integrals. As special cases of these tests, generalized rank and supremum-type tests are considered.