Numerical approximation of stochastic differential equations modeling subdiffusions

Kobayashi Kei, Fordham University

Standard Brownian motion composed with a random time change given by an inverse subordinator has been used to model subdiffusions, where particles spread more slowly than the classical Brownian particles. The time-changed Brownian motion is neither Markovian nor Gaussian, and standard procedures known for normal diffusions do not generally work. This talk gives an overview of the framework of numerical approximation schemes for stochastic differential equations driven by the time-changed Brownian motion and discusses the associated rates of convergence. This is based on joint work with Sixian Jin and Ernest Jum.

Area: CS38 - Subordination and time-changed stochastic processes (Alessandro De Gregorio)

Keywords: time-changed Brownian motion, subdiffusion, stochastic differential equation, numerical approximation

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