On stochastic differential equations with random delay

Details On stochastic differential equations with random delay On stochastic differential equations with random delay

2011-08-05

arxiv.org/abs/1108.1298v2

J. Stat. Mech. (2011) P10008

Physics

Condensed Matter

Statistical Mechanics

22 pages, 6 figures, 1 table. A couple of updates and minor changes

Scientific paper

10.1088/1742-5468/2011/10/P10008

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation with random delay, the corresponding deterministic equation has order $n+1$. We analyze various examples of dynamical systems of this kind, and find a number of unusual behaviors. For instance, for the harmonic oscillator with random delay, the energy grows as $\exp((3/2)\,t^{2/3})$ in reduced units. We then investigate the effect of introducing a discrete time step $\epsilon$. At variance with the continuous situation, the discrete random recursion relations thus obtained have intrinsic fluctuations. The crossover between the fluctuating discrete problem and the deterministic continuous one as $\epsilon$ goes to zero is studied in detail on the example of a first-order linear differential equation.

Affiliated with

Also associated with

No associations

Rating

On stochastic differential equations with random delay does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On stochastic differential equations with random delay, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On stochastic differential equations with random delay will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-668416