Abstract
Abstract: In this article, we prove integration by parts (IBP) formulas concerning maxima of solutions to some stochastic differential equations (SDEs). We will deal with three types of maxima. First, we consider discrete time maximum, and then continuous time maximum in the case of one-dimensional SDEs. Finally, we deal with the maximum of the components of a solution to multi-dimensional SDEs. Applications to study their probability density functions by means of the IBP formulas are also discussed.
Original language | English |
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Pages (from-to) | 293-317 |
Number of pages | 25 |
Journal | Stochastic Analysis and Applications |
Volume | 34 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2016 Mar 3 |
Externally published | Yes |
Keywords
- Malliavin calculus
- maximum process
- probability density function
- stochastic differential equation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics