First passage times of univariate and bivariate diffusion processes to time-varying and constant boundaries: analytical, statistical and numerical results.
Sprache des Vortragstitels:
12th German Probability and Statistics Days - Stochastikhtage Bochum 2016
Sprache des Tagungstitel:
The first passage time (FPT) problem of univariate diffusion processes through constant boundaries is relevant in different fields, e.g. engineering, finance, neuroscience and physics, and it has been extensively studied in the literature. On the contrary, less results are available in presence of time-varying boundaries or for multivariate diffusion processes. In this talk we tackle both problems, investigating the FPT problem of: a) a Wiener process in presence of an exponentially decaying threshold ; b) a two-dimensional correlated diffusion process in presence of some constant boundaries .
 Tamborrino, M. (2016) Approximation of the first passage time density of a Wiener process to an exponentially decaying threshold by two-piecewise linear boundary. Application to neuronal spiking activity. Mathematical Biosciences and Engineering , 13 (3), 613--629, 2016 .
 Sacerdote, L., Tamborrino, M. and Zucca, C. First passage times of two-dimensional correlated processes: analytical results for the Wiener process and a numerical method for diffusion processes. Journal of Computation and Applied Mathematics, 296, 275-292, 2016.