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Showing 1 to 4 of 4 for “"Dyson Series"”.
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An Exponential Formula for Random Variables Generated by Multiple Brownian Motions
<p>The frozen operator has been used to develop Dyson-series like representations for random variables generated by classical Brownian motion, Lévy processes and fractional Brownian with Hurst index greater than 1/2.The relationship between the conditional expectation of a random variable (or …
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A full asymptotic series of European call option prices in the SABR model with beta=1
… calculations. The first approach, which we call "Dyson series on the return's idiosyncratic noise" yields a complete series expansion but necessitates the calculation of a 7-dimensional integral. Two of these dimensions come from the use of Yor's (1992) formula for the joint density of a Brownian …
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Time-Dependent Perturbation and the Born-Oppenheimer Approximation
… Using previous results that develop asymptotic series solutions in the Born-Oppenheimer parameter ε, we derive a formal Dyson series expansion in the perturbation parameter μ, which is proportional to the electromagnetic field strength. We then prove that this series is asymptotically accurate …
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Toward a Rigorous Justification of the Three-Body Impact Parameter Approximation
The impact parameter (IP) approximation is a semiclassical model in quantum scattering theory wherein N large masses interact with one small mass. We study this model in one spatial dimension using the tools of time-dependent scattering theory, considering a system of two large-mass particles and …