Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 12 of 12 for “"Malliavin calculus"”.
-
An application of the Malliavin calculus to infinite dimensional diffusions
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1984.
-
Some application of Malliavin calculus to SPDE and convergence of densities
Some applications of Malliavin calculus to stochastic partial differential equations (SPDEs) and to normal approximation theory are studied in this dissertation. In Chapter 3, a Feynman-Kac formula is established for a stochastic heat equation driven by Gaussian noise which is, with respect to …
-
Malliavin Calculus in the Canonical Levy Process: White Noise Theory and Financial Applications.
We constructed a white noise theory for the Canonical Levy process by Sole, Utzet, and Vives. The construction is based on the alternative construction of the chaos expansion of square integrable random variable. Then, we showed a Clark-Ocone theorem in L^2(P) and under the change of measure. The …
-
Morse inequalities, a probabilistic approach
… the Witten Laplacian has an expression via the Malliavin calculus. The first step is the analysis of this heat kernel at a point away the critical set. Using Markov property, an iteration procedure and estimates on exit times from balls, everything is reduced to the estimation of a solution to a …
-
A full asymptotic series of European call option prices in the SABR model with beta=1
… in the SABR model with beta= 1 case by means of Malliavin Calculus. We follow the approach of Alòs et al (2006) who showed that under stochastic volatility framework, the option prices can be written as the sum of the classic Hull-White (1987) term and a correction due to correlation. We derive …
-
Stable processes: theory and applications in finance
… general derivatives and risk management based on Malliavin calculus. We derive a Bismut-Elworthy-Li (BEL) representation formula for computing financial Greeks under the framework of subordinated Brownian motion by an inverse α-stable process with α ε (0; 1]. This subordination by an inverse …
-
Two topics in financial mathematics : Forward utility and consumption functions & Hedging with variance swaps in infinite dimensions
… to infinite dimensional stochastic analysis, Malliavin calculus and SPDEs in Hilbert spaces.
-
Reciprocal classes of Markov processes : an approach with duality formulae
… Lévy processes, which is well known in Malliavin calculus. We obtain two new methods to prove this duality formula, which are not based on the chaos decomposition of the space of square-integrable function- als. One of these methods uses a formula of partial integration that …
-
Deterministic and Stochastic Approaches to Relaxation to Equilibrium for Particle Systems
… equation with a confining potential via Malliavin calculus. We also look at showing hypocoercivity in relative entropy. In his seminal work work on hypocoercivity Villani obtained results on hypocoercivity in relative entropy for the kinetic Fokker-Planck equation. We review this and …
-
Geometry of sub-Riemannian diffusion processes
Sub-Riemannian geometry is the natural setting for studying dynamical systems, as noise often has a lower dimension than the dynamics it enters. This makes sub-Riemannian geometry an important field of study. In this thesis, we analysis some of the aspects of sub-Riemannian diffusion processes on …
-
On Gaussian multiplicative chaos and conformal field theory
… the integration by parts formula from Malliavin calculus can be interpreted in the context of symplectic geometry and the stress-energy tensor emerges in connection with the momentum map for the Diff(S^1)-action.
-
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 …