Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter ε > 0, are considered. Using an interior Dirichlet heat kernel lower bound estimate for second order elliptic operators in bounded domains from [13], certain uniform in ε lower bounds on transition densities of such constrained diffusions are ...

This paper provides methods for carrying out likelihood based inference on non-linear observed and partially observed non-linear diffusions. The diffusions can potentially be non-stationary. The methods are based on innovative Markov chain Monte Carlo methods combined with an augmentation strategy. We study the performance of the methods as the degree of augmentation goes to infinity and find t...

This paper introduces quasi-maximum likelihood estimator for multivariate diffusions based on discrete observations. A numerical solution to the stochastic differential equation is obtained by higher order Wagner-Platen approximation and it is used to derive the first two conditional moments. Monte Carlo simulation shows that the proposed method has good finite sample property for both normal a...

In this paper we solve the dividend optimization problem for a corporation or a financial institution when the managers of the corporation are facing (regulatory) implementation delays. We consider several cash reservoir models for the firm including two mean-reverting processes, OrnsteinUhlenbeck and square-root processes. Since the cashflow structure of different companies have different qual...

For an arbitrary bounded Lipschitz domain D, we propose a class of discrete analogues for the boundary local time of reflected diffusions in D. These discrete analogues are obtained from random walks on D := D ∩ 2−kZd and can be effectively simulated in practice. We prove weak convergence of the joint law of the random walks and the proposed analogues to the joint law of reflected diffusion and...

In this paper, we construct the two-parameter Feller semigroup associated with a certain one-dimensional inhomogeneous Markov process. This process may be described as follows. At interior points of finite number intervals $(-\infty,r_1(s)),\,(r_1(s),r_2(s)),\ldots,\,(r_{n}(s),\infty)$ separated by $r_i(s)\,(i=1,\ldots,n)$, positions which depend on time variable, coincides ordinary diffusions ...

In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by usi...