Abstract
Multidimensional stochastic models in mathematical finance and so on are now well-studied. As to obtain more properties of them, we focus on some multidimensional discrete distributions in relation to a class of multiple zeta functions. The class called “multidimensional Shintani zeta functions” was first introduced in Aoyama and Nakamura (Tokyo J Math 36:521–538, 2013), where a class of probability distributions called “multidimensional Shintani zeta distributions associated with the zeta functions is definable. In this paper, we show that this class includes many kinds of multidimensional discrete distributions. We pick up some cases of multidimensional Shintani zeta functions and introduce some classes of distributions which contain multinomial and negative multinomial distributions as their generalizations. More precisely, we give some necessary and sufficient conditions for the functions to generate probability distributions in view of zeta functions and consider their infinite divisibilities as well.
| Original language | English |
|---|---|
| Pages (from-to) | 33-50 |
| Number of pages | 18 |
| Journal | Japan Journal of Industrial and Applied Mathematics |
| Volume | 32 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2015 |
| Externally published | Yes |
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Keywords
- Characteristic function
- Infinitely divisible distribution
- Multinomial distribution
- Zeta function
ASJC Scopus subject areas
- Applied Mathematics
- Engineering(all)
Cite this
Multinomial distributions in Shintani zeta class. / Aoyama, Takahiro; Yoshikawa, Kazuhiro.
In: Japan Journal of Industrial and Applied Mathematics, Vol. 32, No. 1, 2015, p. 33-50.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Multinomial distributions in Shintani zeta class
AU - Aoyama, Takahiro
AU - Yoshikawa, Kazuhiro
PY - 2015
Y1 - 2015
N2 - Multidimensional stochastic models in mathematical finance and so on are now well-studied. As to obtain more properties of them, we focus on some multidimensional discrete distributions in relation to a class of multiple zeta functions. The class called “multidimensional Shintani zeta functions” was first introduced in Aoyama and Nakamura (Tokyo J Math 36:521–538, 2013), where a class of probability distributions called “multidimensional Shintani zeta distributions associated with the zeta functions is definable. In this paper, we show that this class includes many kinds of multidimensional discrete distributions. We pick up some cases of multidimensional Shintani zeta functions and introduce some classes of distributions which contain multinomial and negative multinomial distributions as their generalizations. More precisely, we give some necessary and sufficient conditions for the functions to generate probability distributions in view of zeta functions and consider their infinite divisibilities as well.
AB - Multidimensional stochastic models in mathematical finance and so on are now well-studied. As to obtain more properties of them, we focus on some multidimensional discrete distributions in relation to a class of multiple zeta functions. The class called “multidimensional Shintani zeta functions” was first introduced in Aoyama and Nakamura (Tokyo J Math 36:521–538, 2013), where a class of probability distributions called “multidimensional Shintani zeta distributions associated with the zeta functions is definable. In this paper, we show that this class includes many kinds of multidimensional discrete distributions. We pick up some cases of multidimensional Shintani zeta functions and introduce some classes of distributions which contain multinomial and negative multinomial distributions as their generalizations. More precisely, we give some necessary and sufficient conditions for the functions to generate probability distributions in view of zeta functions and consider their infinite divisibilities as well.
KW - Characteristic function
KW - Infinitely divisible distribution
KW - Multinomial distribution
KW - Zeta function
UR - http://www.scopus.com/inward/record.url?scp=84925467439&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84925467439&partnerID=8YFLogxK
U2 - 10.1007/s13160-015-0165-9
DO - 10.1007/s13160-015-0165-9
M3 - Article
AN - SCOPUS:84925467439
VL - 32
SP - 33
EP - 50
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
SN - 0916-7005
IS - 1
ER -