The Pólya process is obtained by embedding the usual (discrete-time) Pólya urn scheme in continuous time. We study the class of tenable Pólya processes of white and blue balls with zero balance (no change in n, the total number of balls, over time). This class includes the...

The dimensional free Harnack inequality is established for a class of semilinear stochastic partial differential equations in the Hilbert space with multiplicative noise by perturbing the linear term of the equation by a suitable linear operator.

This paper applies the theory of Hamilton–Jacobi partial differential equations to the case of first-order traffic flow models. The traffic flow surface is analyzed with respect to the three 2-dimensional coordinate systems arising in the space of vehicle number, time and distance. In each...

We study a tanker chartering decision problem faced by refinery companies. The decision process is formulated as an optimal stopping problem with geometric Brownian motion for the spot freight rate dynamics and a Poisson type arrival process for the tankers. We show the problem can be solved...