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Position distribution in a generalised run and tumble process
[article]
2020
arXiv
pre-print
We study a class of stochastic processes of the type d^n x/dt^n= v_0 σ(t) where n>0 is a positive integer and σ(t)=± 1 represents an 'active' telegraphic noise that flips from one state to the other with a constant rate γ. For n=1, it reduces to the standard run and tumble process for active particles in one dimension. This process can be analytically continued to any n>0 including non-integer values. We compute exactly the mean squared displacement at time t for all n>0 and show that at late
arXiv:2009.01487v1
fatcat:zmubrrls75dt7bmu45lws4dggu