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
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U2 - 10.1080/07362994.2015.1129346
DO - 10.1080/07362994.2015.1129346
M3 - Article
AN - SCOPUS:84959100319
SN - 0736-2994
VL - 34
SP - 293
EP - 317
JO - Stochastic Analysis and Applications
JF - Stochastic Analysis and Applications
IS - 2
ER -