@article{Gaengaew_Jantai_Kooakachai_2024, title={Some Properties of a Trinomial Random Walk Conditioned on End Points: Annual Meeting in Mathematics 2023}, volume={22}, url={https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1610}, abstractNote={<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&nbsp;$(X_1, X_2, \ldots, X_n)$ 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>}, number={1}, journal={Thai Journal of Mathematics}, author={Gaengaew, Poramin and Jantai, Wasamon and Kooakachai, Monchai}, year={2024}, month={Mar.}, pages={203–216} }