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 |
|---|---|
| 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 |
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Keywords
- Malliavin calculus
- maximum process
- probability density function
- stochastic differential equation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics
Cite this
Integration by parts formulas concerning maxima of some SDEs with applications to study on density functions. / Nakatsu, Tomonori.
In: Stochastic Analysis and Applications, Vol. 34, No. 2, 03.03.2016, p. 293-317.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Integration by parts formulas concerning maxima of some SDEs with applications to study on density functions
AU - Nakatsu, Tomonori
PY - 2016/3/3
Y1 - 2016/3/3
N2 - 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.
AB - 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.
KW - Malliavin calculus
KW - maximum process
KW - probability density function
KW - stochastic differential equation
UR - http://www.scopus.com/inward/record.url?scp=84959100319&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84959100319&partnerID=8YFLogxK
U2 - 10.1080/07362994.2015.1129346
DO - 10.1080/07362994.2015.1129346
M3 - Article
AN - SCOPUS:84959100319
VL - 34
SP - 293
EP - 317
JO - Stochastic Analysis and Applications
JF - Stochastic Analysis and Applications
SN - 0736-2994
IS - 2
ER -