# zbMATH — the first resource for mathematics

On the distribution of the position of a randomly accelerated particle. (English) Zbl 0923.60059
Theory Probab. Math. Stat. 56, 167-174 (1998) and Teor. Jmovirn. Mat. Stat. 56, 161-168 (1997).
The authors consider the process $$X(t)=A(0)\int_0^t(t-s)(-1)^{N(s)}ds$$, where $$N(t)$$ denotes the number of events of a homogeneous Poisson process in $$[0,t],$$ and the random variable (independent of $$N(t)$$) $$A(0)$$ takes values $$\pm a$$ with probability $$1/2$$. This process is used for modelling a uniformly accelerated one-dimensional motion. The authors derive recurrent relationships for the conditional distributions $$P(X(t)\leq x\mid N(t)=n)$$, $$n=1,2,\dots$$ . The limit behaviour of such conditional distributions is investigated.

##### MSC:
 60G70 Extreme value theory; extremal stochastic processes