Properties of integrals with respect to fractional Poisson processes with compact kernels

Анотація

Properties of a fractional Poisson process with the Molchan–Golosov kernel are studied. The kernel can be viewed as compact since it is non-zero on a compact interval. The integral of a nonrandom function with respect to centered and non-centered fractional Poisson processes with the Molchan–Golosov kernel is introduced. The second moments of these integrals are obtained in terms of the norm of the integrand in the space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Subscript 1 slash upper H Baseline left-parenthesis left-bracket 0 comma upper T right-bracket right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo stretchy="false">]</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">L_{1/H}([0,T])</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . Moment estimates for higher moments of these integrals are established by using the Bichteler–Jacod inequality.

Класифікація

Ідентифікатори

Схожі роботи