Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 41: Brownian Motion, Stochastic Processes, Transport II

DY 41.11: Talk

Friday, March 18, 2011, 13:00–13:15, HÜL 186

Exact solution of a stochastic birth and death process with delayed death — •Luis F. Lafuerza and Raul Toral — Intitute for Cross-Disciplinary Physics and Complex Systems

Motivated by protein dynamics where degradation can occur with a time delay, we study a stochastic birth and death process with delayed-degradation. This is one of the simplest rocesses in which the interplay between stochasticity and delay can be studied.

In this work we develop a rigorous derivation of the stochastic description of a birth and death process that includes delay and solve it exactly. We find that the exact solution for the probabilities leads to equations for the mean values that do not comply with simple intuitive arguments and that oscillatory behavior does not exist (while it is usually assumed to be present in this type of system). This warns about the derivation of dynamical equations describing the evolution of the concentrations in cases in which delay plays a role.