29
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Simulation and estimation for the fractional Yule process

      Preprint

      Read this article at

          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          In this paper, we propose some representations of a generalized linear birth process called fractional Yule process (fYp). We also derive the probability distributions of the random birth and sojourn times. The inter-birth time distribution and the representations then yield algorithms on how to simulate sample paths of the fYp. We also attempt to estimate the model parameters in order for the fYp to be usable in practice. The estimation procedure is then tested using simulated data as well. We also illustrate some major characteristics of fYp which will be helpful for real applications.

          Related collections

          Most cited references11

          • Record: found
          • Abstract: not found
          • Article: not found

          Fractional Poisson processes and related planar random motions

            Bookmark
            • Record: found
            • Abstract: found
            • Article: found
            Is Open Access

            Fractional diffusion equations and processes with randomly varying time

            In this paper the solutions \(u_{\nu}=u_{\nu}(x,t)\) to fractional diffusion equations of order \(0<\nu \leq 2\) are analyzed and interpreted as densities of the composition of various types of stochastic processes. For the fractional equations of order \(\nu =\frac{1}{2^n}\), \(n\geq 1,\) we show that the solutions \(u_{{1/2^n}}\) correspond to the distribution of the \(n\)-times iterated Brownian motion. For these processes the distributions of the maximum and of the sojourn time are explicitly given. The case of fractional equations of order \(\nu =\frac{2}{3^n}\), \(n\geq 1,\) is also investigated and related to Brownian motion and processes with densities expressed in terms of Airy functions. In the general case we show that \(u_{\nu}\) coincides with the distribution of Brownian motion with random time or of different processes with a Brownian time. The interplay between the solutions \(u_{\nu}\) and stable distributions is also explored. Interesting cases involving the bilateral exponential distribution are obtained in the limit.
              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Parameter estimation for fractional Poisson processes

                Bookmark

                Author and article information

                Journal
                10.1007/s11009-010-9207-6
                1303.6681

                Probability
                Probability

                Comments

                Comment on this article