TY - JOUR
AU - Gaengaew, Poramin
AU - Jantai, Wasamon
AU - Kooakachai, Monchai
PY - 2024/03/31
Y2 - 2024/06/14
TI - Some Properties of a Trinomial Random Walk Conditioned on End Points: Annual Meeting in Mathematics 2023
JF - Thai Journal of Mathematics
JA - Thai J Math
VL - 22
IS - 1
SE - Articles
DO -
UR - https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1610
SP - 203–216
AB - <p>Given a sequence of trinomial random variables $\displaystyle\{ X_i \}^\infty_{i=1}$ and define $S_n =\sum_{i=1}^n X_i$ and $S_0 = 0$, we study some properties of $X_i $ conditioned on $S_n = 0.$ The mathematical expressions of expectation, variance and covariance were investigated. We found that the a finite sequence $(X_1, X_2, \ldots, X_n)$ conditioned on $S_n = 0$ is exchangeable. Moreover, the expectation of $X_i$ is zero and the covariance of $X_i$ and $X_j$ where $i
eq j$ is nonpositive. Furthermore, we extend the previous setting to a rescaled trinomial random walk. Some properties on the extension were derived.</p>
ER -