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The aim of this paper is to establish sharp estimates for the moduli of continuity of the local time of a class of sub-fractional Brownian motions. We also investigate the continuity of their local times with respect to the self-similarity index. [ABSTRACT FROM AUTHOR]

We consider one-dimensional stochastic equations involving local times of unknown processes. We interpret these equations as diffusion in layered media with semi-permeable barriers and we study the limit behavior of solutions as barriers compress in one barrier. Conditions for convergence in law and limit equation are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study a one-dimensional random motion with switching process having an Erlang-3 distribution for the sojourn times. We obtain the solution of the associated hyperbolic PDE of sixth order through algebraic techniques. [ABSTRACT FROM AUTHOR]

In this paper we prove two main results. The first one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index . Our result is similar to that of Marcus and Rosen in 1992 for local time. The second result is to give a ( p, q)-variation of fractional derivatives of local time of symmetric stable process with index . Our approach is similar to that of Eisenbaum in 2000 for local time. [ABSTRACT FROM AUTHOR]

We introduce Monte Carlo methods to compute the solution of elliptic equations with pure Neumann boundary conditions. We first prove that the solution obtained by the stochastic representation has a zero mean value with respect to the invariant measure of the stochastic process associated to the equation. Pointwise approximations are computed by means of standard and new simulation schemes especially devised for local time approximation on the boundary of the domain. Global approximations are computed thanks to a stochastic spectral formulation taking into account the property of zero mean value of the solution. This stochastic formulation is asymptotically perfect in terms of conditioning. Numerical examples are given on the Laplace operator on a square domain with both pure Neumann and mixed Dirichlet-Neumann boundary conditions. A more general convection-diffusion equation is also numerically studied. [ABSTRACT FROM AUTHOR]

In this paper, we prove two main results. The first one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index ; our result is similar to that of Marcus and Rosen (1992) for local time. The second result is to give a -variation of fractional derivatives of local time of symmetric stable process with index . Our approach is similar to that of Eisenbaum (2000) for local time. [ABSTRACT FROM AUTHOR]

This paper extends the previous probability model for the distribution of lead time in periodic cancer screening exams, namely, in that the lifetime T is treated as a random variable, instead of a fixed value. Hence the number of screens for a given individual is a random variable as well. We use the actuarial life table from the Social Security Administration to obtain the lifetime distribution, and then use this information to project the lead time distribution for someone with a future screening schedule. Simulation studies using the HIP study group data provide estimates of the lead time under different screening frequencies. The projected lead time has two components: a point mass at zero (corresponding to interval cases detected between screening exams) and a continuous probability density. We present estimates of the projected lead time for participants in a breast cancer screening program. The model is more realistic and can inform optimal screening frequency. This study focuses on breast cancer screening, but is applicable to other kinds of cancer screening also. [ABSTRACT FROM AUTHOR]

The restriction of an isotropic α-stable Lévy process Xα in ℝ n on the fractal support F of certain finite Borel measures μ is introduced in three different ways: by means of the trace of its Dirichlet form on F and related Besov spaces, by its μ-local time on F and the corresponding time changed process, and by restricting on the fine support of μ via balayage spaces and potentials. Moreover, for compact upper d-regular sets F with d > n − α an approximation by means of restrictions of Xα to small ℇ-neighborhoods of F is given. [ABSTRACT FROM AUTHOR]