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The interest in orthogonal polynomials and random Fourier series in numerousbranches of science and a few studies on random Fourier series in orthogonalpolynomials inspired us to focus on random Fourier series in Jacobipolynomials. In the present note, an attempt has been made to investigate thestochastic convergence of some random Jacobi series. We looked into the randomseries $\sum_{n=0}^\infty d_n r_n(\omega)\varphi_n(y)$ in orthogonalpolynomials $\varphi_n(y)$ with random variables $r_n(\omega).$ The randomcoefficients $r_n(\omega)$ are the Fourier-Jacobi coefficients of continuousstochastic processes such as symmetric stable process and Wiener process. The$\varphi_n(y)$ are chosen to be the Jacobi polynomials and their variantsdepending on the random variables associated with the kind of stochasticprocess. The convergence of random series is established for differentparameters $\gamma,\delta$ of the Jacobi polynomials with corresponding choiceof the scalars $d_n$ which are Fourier-Jacobi coefficients of a suitable classof continuous functions. The sum functions of the random Fourier-Jacobi seriesassociated with continuous stochastic processes are observed to be thestochastic integrals. The continuity properties of the sum functions are alsodiscussed.

On the Convergence of Random Fourier-Jacobi Series of Continuous functions