Peter Baxendale Professor of Mathematics Contact Information E-mail: baxendal@math.usc.edu Phone: (213) 740-3789 Office: KAP 424B LINKS Faculty Profile on Departmental Website

Academic Appointment, Affiliation, and Employment History

Tenure Track Appointments

• Professor of Mathematics, University of Southern California, 08/01/1988-  
• Associate Professor of Mathematics, University of Florida, 08/01/1987-08/01/1988  
• Lecturer in Mathematics, University of Aberdeen, Scotland, 09/01/1973-09/01/1987  

Non-Tenure Track Appointments

• Lecturer in Mathematics, University of Warwick, England, 01/01/1972-01/01/1973  

Description of Research

Summary Statement of Research Interests

Publications

Book Chapter

• Baxendale, P. H. (1999). Stability along trajectories at a stochastic bifurcation point. pp. p. 1-25.. Stochastic Dynamics/Springer.

Journal Article

• Baxendale, P. H., Mayberry, J. (2009). A Spectral Analysis of the Sequence of Firing Phases in Stochastic Integrate-and-Fire Oscillators. Stochastic Processes and Applications.
• Baxendale, P. H., Dimitroff, G. (2009). Uniform shrinking and expansion under isotropic Brownian flows. Journal of Theoretical Probability. Vol. 22, pp. 620-–639..
• Baxendale, P. H., Picas, M. (2007). Almost sure and moment Lyapunov exponents for a stochastic beam equation. Journal of Functional Analysis. Vol. 243, pp. 566-610.
• Baxendale, P. H. (2005). Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Annals of Applied Probability. Vol. vol 15 (2005), pp. pp 700-738.
• Baxendale, P. H. (2004). Stochastic averaging and asymptotic behavior of the stochastic Duffing-van der Pol equation. Stochastic Processes and Their Applications/Elsevier. Vol. vol 113 (2004), pp. pp 235-272.
• Baxendale, P. H., Liptser, R., Chigansky, P. (2004). Asymptotic stability of the Wonham filter: ergodic and non-ergodic signals. SIAM Journal on Control and Optimization/SIAM. Vol. vol 43, pp. pp. 643-669..
• Baxendale, P. H., Goukasian, L. (2002). Lyapunov exponents for small random perturbations of Hamiltonian systems. Annals of Probability. Vol. vol 30, pp. pp. 101-134..
• Baxendale, P. H. (1994). A stochastic Hopf bifurcation. Probability Theory and Related Fields/Springer. Vol. vol 99, pp. pp. 581-616..

Proceedings

• Baxendale, P. H. (2005). Random sources and sinks for stochastic dynamical systems. Proceedings of ENOC-2005, Fifth EUROMECH Nonlinear Dynamics Conference/Eindhoven University of Technology, The Netherlands.
• Baxendale, P. H. (2003). Lyapunov exponents and stability for the stochastic Duffing-van der Pol oscillator. pp. p. 125-135. IUTAM Symposium on Nonlinear Stochastic Dynamics (N. Sri Namachchivaya and Y.K. Lin, eds)/Kluwer Academic Publications (Kluwer).
• Baxendale, P. H. (1991). Invariant measures for nonlinear stochastic differential equations. pp. pp. 123-140. Lyapunov Exponents. Proc. Oberwolfach 1990 (L. Arnold, H. Crauel and J.-P. Eckmann eds)/Springer.

Honors and Awards

• Fellow (or Equivalent) of National Society in Discipline, Fellow of Institute of Mathematical Statistics, 1993-  

Service to the Profession

Editorships and Editorial Boards

• Member of the editorial board, Stochastics and Dynamics, 2001-2008  

Professional Memberships

• Institute of Mathematical Statistics, 1989-  
• American Mathematical Society, 1987-  
• London Mathematical Society, 1972-