Flows and stochastic Taylor series in Itô calculus

Flows and stochastic Taylor series in Itô calculus

Fractional Calculus and the Taylor-riemann Series

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Tayl...

Sensitivity analysis using Itô-Malliavin calculus and application to stochastic optimal control

Itô versus Stratonovich calculus in random population growth.

The context is the general stochastic differential equation (SDE) model dN/dt=N(g(N)+sigmaepsilon(t)) for population growth in a randomly fluctuating environment. Here, N=N(t) is the population size at time t, g(N) is the 'average' per capita growth rate (we work with a general almost arbitrary function g), and sigmaepsilon(t) is the effect of environmental fluctuations (sigma>0, epsilon(t) sta...

External and Internal Incompressible Viscous Flows Computation using Taylor Series Expansion and Least Square based Lattice Boltzmann Method

The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...