We consider a bivariate diffusion process and we study the first passage time of one
component through a boundary. We prove that its probability density is the unique solution …

Due to different circumstances of production, two nations can produce similar goods and
services at different prices. They can both benefit by getting involved in international trade to …

Let be $ X (t)= x-\mu t+\sigma B_t-N_t $ a L $\acute {\text {e}} $ vy process starting from $ x>
0, $ where $\mu\ge 0,\\sigma\ge 0,\B_t $ is a standard BM, and $ N_t $ is a homogeneous …

To investigate the complex dynamics of a biological neuron that is subject to small random
perturbations we can use stochastic neuron models. While many techniques have already …

We propose two different algorithms to solve high dimensional Dirichlet problems numeri¬
cally. Both approaches are based on the stochastic representation of the solution in the form …

Il cervello umanoe indubbiamente la struttura piu complessa del vivente: con le parole di
Charles Darwine “il piu alto risultato [dell'evoluzione] che si possa concepire” e la …

I am deeply grateful to my advisor, Dr. Pak-Wing Fok, for his instructive guidance, useful
advice, and support throughout my research. I really appreciate his patience and help over …

A discrete computer simulation of an Itô SDE is a necessary computational tool for the study
of the behavior of diffusing particles in situations in which the FPE does not provide the …

In this paper, we develop a Monte Carlo based algorithm for estimating the FPT density of a
time-homogeneous SDE through a time-dependent frontier. We consider Brownian bridges …

The aim of this contribution is to present basic mathematical knowledge on how the hazard
rate of the first hitting time is related to the underlaying stochastic process. We would not …