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Time-Space Harmonic Polynomials For Stochastic Processes., Arindam Sengupta Dr.
Time-Space Harmonic Polynomials For Stochastic Processes., Arindam Sengupta Dr.
Doctoral Theses
The sequence of polynomials of a single variable known as the Hermite polynomialshala) = ), k21, (-1)* ha(z) =has many close links with the Normal distribution. Their association goes very doep, and extends to several connections bet ween the two-variable Hermite polynomialsHll, 2) = the(z/t), . k21.and the prime example of Gaussian processes, that is Brownian motion, as well. Much of this connection stems from what we term the time-space harmonic property of these polynomials for the Brownian motion process. An exact definition of this property follows later. A natural question that arises is, for stochastic processes in general, when …