Random walk over a hypersphere
In a recent paper the author had shown that a special case of S. M. Joshi transform (so named after the author's reverent father) of distributions (Sba f)(x)=〈f(y), lFl(a0;b0;ixy) lFl(a;b;−2ixy)〉 is a characteristic function of a spherical distribution. Using the methods developed in that pa...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1985-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171285000758 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849307441015029760 |
|---|---|
| author | J. M. C. Joshi |
| author_facet | J. M. C. Joshi |
| author_sort | J. M. C. Joshi |
| collection | DOAJ |
| description | In a recent paper the author had shown that a special case of S. M. Joshi
transform (so named after the author's reverent father) of distributions
(Sba f)(x)=〈f(y), lFl(a0;b0;ixy) lFl(a;b;−2ixy)〉
is a characteristic function of a spherical distribution. Using the methods developed in that paper; the problem of distribution of the distance CD, where C and D are points niformly distributed in a hypersphere, has been discussed in the present paper. The form of characteristic function has also been obtained by the method of projected distribution.
A generalization of Hammersley's result has also been developed. The main purpose of the paper is to show that although the use of characteristic functions, using the method of Bochner, is available in problems of random walk yet distributional S. M. Joshi transform can be used as a natural tool has been proved for the first time in the paper. |
| format | Article |
| id | doaj-art-210960f3aa0846ad867e341231be69da |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-210960f3aa0846ad867e341231be69da2025-08-20T03:54:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018468368810.1155/S0161171285000758Random walk over a hypersphereJ. M. C. Joshi0Shipra Sadan, G. I. C. Road, Pittogarab, U. P. 262501, IndiaIn a recent paper the author had shown that a special case of S. M. Joshi transform (so named after the author's reverent father) of distributions (Sba f)(x)=〈f(y), lFl(a0;b0;ixy) lFl(a;b;−2ixy)〉 is a characteristic function of a spherical distribution. Using the methods developed in that paper; the problem of distribution of the distance CD, where C and D are points niformly distributed in a hypersphere, has been discussed in the present paper. The form of characteristic function has also been obtained by the method of projected distribution. A generalization of Hammersley's result has also been developed. The main purpose of the paper is to show that although the use of characteristic functions, using the method of Bochner, is available in problems of random walk yet distributional S. M. Joshi transform can be used as a natural tool has been proved for the first time in the paper.http://dx.doi.org/10.1155/S0161171285000758 |
| spellingShingle | J. M. C. Joshi Random walk over a hypersphere International Journal of Mathematics and Mathematical Sciences |
| title | Random walk over a hypersphere |
| title_full | Random walk over a hypersphere |
| title_fullStr | Random walk over a hypersphere |
| title_full_unstemmed | Random walk over a hypersphere |
| title_short | Random walk over a hypersphere |
| title_sort | random walk over a hypersphere |
| url | http://dx.doi.org/10.1155/S0161171285000758 |
| work_keys_str_mv | AT jmcjoshi randomwalkoverahypersphere |