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- W2030393559 abstract "We consider two independent symmetric Markov random flights Z 1(t) and Z 2(t) performed by the particles that simultaneously start from the origin of the Euclidean plane $mathbb{R}^{2}$ in random directions distributed uniformly on the unit circumference S 1 and move with constant finite velocities c 1>0, c 2>0, respectively. The new random directions are taking uniformly on S 1 at random time instants that form independent homogeneous Poisson flows of rates λ 1>0, λ 2>0. The probability distribution function $varPhi(r,t)= operatorname{Pr} { rho(t)<r }$ of the Euclidean distance $$rho(t)=bigVert mathbf{Z}_1(t) - mathbf{Z}_2(t) bigVert , quad t>0, $$ between Z 1(t) and Z 2(t) at arbitrary time instant t>0, is derived. Asymptotics of Φ(r,t), as r→0, and a numerical example are also given." @default.
- W2030393559 created "2016-06-24" @default.
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- W2030393559 date "2013-12-19" @default.
- W2030393559 modified "2023-10-16" @default.
- W2030393559 title "Probability Law for the Euclidean Distance Between Two Planar Random Flights" @default.
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- W2030393559 doi "https://doi.org/10.1007/s10955-013-0901-y" @default.
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