Abstract:
We consider a homogeneous process $S(t)$ on $[0,\infty)$ with independent increments, establish the local and ordinary large deviation principles for the trajectories of the processes $s_T(t):=\frac1TS(tT)$, $t\in[0,1]$, as $T\to\infty$, and obtain a series of inequalities for the distributions of the trajectories of $S(t)$.
Keywords:process with independent increments, Cramer's condition, function of deviations, large deviation principle (LDP), local large deviation principle (local LDP), Chebyshev-type inequality, convex set.