Empirical studies of structural credit risk models so far are often based on calibration, rolling estimation, or regressions. This paper proposes a GMM-based method that allows us to both consistently estimate the model parameters and test whether all the restrictions of the model are satisfied....

We study the small deviation problem for a class of symmetric Lévy processes, namely, subordinated Lévy processes. These processes can be represented as WoA, where W is a standard Brownian motion, and A is a subordinator independent of W. Under some mild general assumption, we give precise...

We present an accurate description for the location of maximum of d-dimensional Brownian motion. In case d = 1, this is a well-known theorem of Csáki et al. (1987a). We also deduce, as application, a version of the iterated logarithm law for the favourite site of transient Brownian motion.

In random environments, the most elementary processes are Sinai's simple random walk and Brox's diffusion process, respectively in discrete and continuous time settings. The two processes are often considered as a kind of companions, somewhat in the same way as the usual random walk and Brownian...

The basic coalescing random walk is a system of interacting particles. These particles start from every site of , and each moves independently as a continuous-time random walk. When two particles visit the same site, they coalesce into a single particle. We are interested in: (a) the radius...

We present a strong approximation of two-dimensional Kesten-Spitzer random walk in random scenery by Brownian motion.

We study the occupation measure of various sets for a symmetric transient random walk in Zd with finite variances. Let denote the occupation time of the set A up to time n. It is shown that tends to a finite limit as n--[infinity]. The limit is expressed in terms of the largest eigenvalue of a...

We characterize the upper and lower functions of a real-valued Wiener process normalized by the supremum of its local times.

We prove a strong approximation for the spatial Kesten-Spitzer random walk in random scenery by a Wiener process.