On the Duality between Coalescing Brownian Particles and the Heat Equation Driven by Fisher-Wright Noise

Tim Hobson (University of Warwick, UK)
Rodge Tribe (University of Warwick, UK)

Abstract


This paper concerns the Markov process duality between the one-dimensional heat equation driven by Fisher-Wright white noise and slowly coalescing Brownian particles. A representation is found for the law of the solution $x \to U(t,x)$ to the stochastic PDE, at a fixed time, in terms of a labelled system of such particles.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 136-145

Publication Date: July 13, 2005

DOI: 10.1214/ECP.v10-1143

References

  1. S. Athreya and R. Tribe. Uniqueness for a class of one-dimensional stochastic PDEs using moment duality. Ann. Probab. 28 (2002), 1711-1734. Math. Review 2002b:60108
  2. E. Donnelly, S.N. Evans, K. Fleischmann, T.G. Kurtz and X. Zhou. Continuum-sites stepping-stone models, coalescing exchangeable partitions and random trees. Ann. Probab. 28 (2000), 1063-1110. Math. Review 2001j:60183
  3. S.N. Ethier and T.G. Kurtz. Markov Processes: Characterization and Convergence. Wiley, New York (1986). Math. Review 88a:60130
  4. T Hobson. Warwick University Ph.D. thesis, in preparation. Math. Review number not available.
  5. C. Mueller and R. Tribe. Stochastic p.d.e.'s arising from the long range contact and long range voter processes. Probab. Theory Related Fields 102 (1995), 519-545. Math. Review 96k:60259
  6. E. Pardoux. Stochastic partial differential equations, a review. Bull. Sci. Math. 117 (1993), 29-47. Math. Review 94i:60071
  7. T. Shiga. Stepping stone models in population genetics and population dynamics. Stochastic Processes Phys. Engng. Math. Appl. 42 (1988), 345-355. Math. Review 89g:92030
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.