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Title: On a class of measures on configuration spaces
Author: ul Haq, Ahsan
ISNI:       0000 0004 2728 631X
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2012
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In this thesis we have explored a new class of measures $\nu_{theta}$ on configuration spaces $\Gamma_X$ (of countable subsets of Euclidean space $X=\mbb{R}^d$), obtained as a push-forward of ``lattice'' Gibbs measure $\theta$ on $X^{\mbb{Z}^d}$. For these measures, we have proved the finiteness of the first and second moments and the integration by parts formula. It has also been proved that the generator of the Dirichlet form of $\nu_{\theta}$ satisfies log-Sobolev inequality, which is not typical for measures on configuration spaces. Stochastic dynamics of a particle in random environment distributed according to the measure $\nu_{\theta}$, is presented as an example of possible application of this construction. We consider a toy model of a market, where this stochastic dynamics represents the volatility process of certain European derivative security. We have derived the ``Black-Scholes type" pricing partial differential equation for this derivative security.
Supervisor: Daletskii, Alexei Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available