Some properties of random fields with independent increments. (Russian) Zbl 0699.60067

Mishura, Yu. S.

Teor. Veroyatn. Mat. Stat., Kiev 41, 56-66 (1989).

The paper contains the canonical decomposition of a strong semimartingale \(x=(x_ t\), \(t\in R^ 2_+)\) with independent increments. The main result is: \[ x_ t=M^ c_ t+B_ t+\int_{[0,t]}\int_{| u| \leq 1}u(\mu_ x-\nu_ x)(ds,du)+\int \quad_{[0,t]}u \mu_ x(ds,du), \] where \(M^ c_ t\) is a continuous strong martingale with independent increments, \(B_ t\) is a nonrandom function of bounded variation, \(\mu_ x\) is the measure of jumps of x, and \(\nu_ x\) is its nonrandom compensator. The representation of the characteristic function of x is also given in terms of semi-invariants.

Reviewer: Yu.S.Mishura

MSC:

60J99	Markov processes
60G60	Random fields

Keywords:

decomposition of a strong semimartingale; independent increments; nonrandom compensator; characteristic function; semi-invariants