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Probability Theory has strong connections with many areas in Analysis. In recent years, many classical results have been restudied by Probabilists (e.g. P.A. Meyer and N. Varopoulos) and alternative proofs have been introduced using powerful tools of Martingale Theory. In particular, one can use Brownian Motion, a continuous stochastic process, to define harmonic functions in classical sense. In this talk, we replace Brownian Motion with a more general process, namely a symmetric stable process. Stable processes are not continuous as Brownian Motion is. But they still enjoy many nice properties. Using this process we define what a ”harmonic” function with respect to this process is and discuss operators obtained through these new ”harmonic” functions. We will discuss some operators which are originated from classical Littlewood-Paley theory. They are used in analysis of singular integral operators. We consider their modification with respect to this discontinuous stochastic process to generalise classic results. We discuss their boundedness on Lp spaces, and discuss a multiplier theorem obtained through these new operators.