An asymptotic expansion in the case of a stable approximating law

Mitalauskas, A.; Statulevičius, V.

doi:10.1007/bf00968375

Cited by 8 publications

(5 citation statements)

References 1 publication

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“…Since y, 5 v,, in our result the quality of the pseudomoment characteristic f, is better than in (5). Since y, 5 v,, in our result the quality of the pseudomoment characteristic f, is better than in (5).…”

Section: (4)supporting

confidence: 47%

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Non‐uniform Estimates in Asymptotic Expansions with a Stable Limit Distribution

Christoph

1991

Mathematische Nachrichten

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Section: (4)supporting

confidence: 47%

“…In the proof If,(r)l 5 e-', for It[ 2 6'n"' (see (61) of [5]) is used with some positive constants 6 and 6' and C in (5) depends on them. Hence, C depends on F, too.…”

Section: (4)mentioning

confidence: 99%

Non‐uniform Estimates in Asymptotic Expansions with a Stable Limit Distribution

Christoph

1991

Mathematische Nachrichten

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“…Such results have been thoroughly studied in the scalar case, see e.g. Mitalauskas and Statuljavičjus [MS76] or the monograph by Christoph and Wolf [CW92]. We also refer to the PhD.…”

Section: Perspectivesmentioning

confidence: 99%

Weak error for Continuous Time Markov Chains related to fractional in time P(I)DEs

Kelbert

Konakov

Menozzi

2016

Stochastic Processes and their Applications

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We provide sharp error bounds for the difference between the transition densities of some multidimensional Continuous Time Markov Chains (CTMC) and the fundamental solutions of some fractional in time Partial (Integro) Differential Equations (P(I)DEs). Namely, we consider equations involving a time fractional derivative of Caputo type and a spatial operator corresponding to the generator of a non degenerate Brownian or stable driven Stochastic Differential Equation (SDE).

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“…Moreover, for pseudomoments a moment inequality holds (see [22]) Further, if v, < 00, then f ( t ) -gab@) is [r]-times differentiable and ICf(t) -gab(t))"'l S v,, k 5 [I].…”

Section: Moments and Pseudomomentsmentioning

confidence: 99%