Malliavin calculus for difference approximations of multidimensional diffusions: Truncated local limit theorem
For difference approximations of multidimensional diffusions, the truncated local limit theorem is proved. Under very mild conditions on the distributions of difference terms, this theorem states that the transition probabilities of these approximations, after truncation of some asymptotically neg...
Збережено в:
| Дата: | 2008 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/164486 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Malliavin calculus for difference approximations of multidimensional diffusions: Truncated local limit theorem / A.M. Kulik // Український математичний журнал. — 2008. — Т. 60, № 3. — С. 340–381. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | For difference approximations of multidimensional diffusions, the truncated local limit theorem is proved.
Under very mild conditions on the distributions of difference terms, this theorem states that the transition
probabilities of these approximations, after truncation of some asymptotically negligible terms, possess
densities that converge uniformly to the transition probability density for the limiting diffusion and
satisfy certain uniform diffusion-type estimates. The proof is based on a new version of the Malliavin
calculus for the product of a finite family of measures that may contain non-trivial singular components.
Applications to the uniform estimation of mixing and convergence rates for difference approximations
of stochastic differential equations and to the convergence of difference approximations of local times of
multidimensional diffusions are given. |
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