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

M. Kelbert; V. Konakov; S. Menozzi

doi:10.1016/j.spa.2015.10.013

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

M. Kelbert
, V. Konakov
, S. Menozzi

National Research University
Université d'Evry Val d'Essonne

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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).

Original language	English
Pages (from-to)	1145-1183
Number of pages	39
Journal	Stochastic Processes and their Applications
Volume	126
Issue number	4
DOIs	https://doi.org/10.1016/j.spa.2015.10.013
Publication status	Published - 1 Apr 2016
Externally published	Yes

Keywords

Fractional Cauchy problems
Local Limit Theorems
Probabilistic approximations
Stable processes

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10.1016/j.spa.2015.10.013

Cite this

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abstract = "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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AU - Kelbert, M.

AU - Konakov, V.

AU - Menozzi, S.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - 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).

AB - 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).

KW - Fractional Cauchy problems

KW - Local Limit Theorems

KW - Probabilistic approximations

KW - Stable processes

UR - https://www.scopus.com/pages/publications/84958926809

U2 - 10.1016/j.spa.2015.10.013

DO - 10.1016/j.spa.2015.10.013

M3 - Article

AN - SCOPUS:84958926809

SN - 0304-4149

VL - 126

SP - 1145

EP - 1183

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 4

ER -

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

Abstract

Keywords

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