Stochastic Analysis Seminar
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Mon, 03/05/2004 14:15 |
Ma Zhi-Ming |
Stochastic Analysis Seminar  |
DH 3rd floor SR |
| The celebrated Levy-Khintchine formula provides us an explicit structure of Levy processes on $R^d$. In this talk I shall present a structure result for quasi-regular semi-Dirichlet forms, i.e., for those semi-Dirichlet forms which are associated with right processes on general state spaces. The result is regarded as an extension of Levy-Khintchine formula in semi-Dirichlet forms setting. It can also be regarded as an extension of Beurling-Deny formula which is up to now available only for symmetric Dirichlet forms. | |||
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Mon, 03/05/2004 15:45 |
Svante Janson (University of Uppsala) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| The Brownian snake (with lifetime given by a normalized Brownian excursion) arises as a natural limit when studying random trees. This may be used in both directions, i.e. to obtain asymptotic results for random trees in terms of the Brownian snake, or, conversely, to deduce properties of the Brownian snake from asymptotic properties of random trees. The arguments are based on Aldous' theory of the continuum random tree. I will discuss two such situations: 1. The Wiener index of random trees converges, after suitable scaling, to the integral (=mean position) of the head of the Brownian snake. This enables us to calculate the moments of this integral. 2. A branching random walk on a random tree converges, after suitable scaling, to the Brownian snake, provided the distribution of the increments does not have too large tails. For i.i.d increments Y with mean 0, a necessary and sufficient condition is that the tails are o(y^{-4}); in particular, a finite fourth moment is enough, but weaker moment conditions are not. | |||
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Mon, 10/05/2004 14:15 |
Touzi Nizar |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| We formulate a problem of super-hedging under gamma constraint by taking the portfolio process as a controlled state variable. This leads to a non-standard stochastic control problem. An intuitive guess of the associated Bellman equation leads to a non-parabolic PDE! A careful analysis of this problem leads to the study of the small time behaviour of double stochastic integrals. The main result is a characterization of the value function of the super-replication problem as the unique viscosity solution of the associated Bellman equation, which turns out to be the parabolic envelope of the above intuitive guess, i.e. its smallest parabolic majorant. When the underlying stock price has constant volatility, we obtain an explicit solution by face-lifting the pay-off of the option. | |||
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Mon, 10/05/2004 15:45 |
James Martin (Paris VII) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 17/05/2004 14:15 |
Ofer Zeitouni |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 17/05/2004 15:45 |
Ron Doney |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| The question whether the measure of a Levy process starting from x>0 and "conditioned to stay positive" converges to the corresponding obiect for x=0 when x tends to 0 is rather delicate. I will describe work with Loic Chaumont which settles this question, essentially in all cases of interest. As an application, I will show how to use this result and excursion theory to give simpler proofs of some recent results about the exit problem for reflected processe derived from spectrally one-sided Levy processes due to Avram. Kyprianou and Pistorius. | |||
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Mon, 24/05/2004 14:15 |
Vincent Vigon |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 24/05/2004 15:45 |
Laure Coutin (Laboratoire de Statistique et Probabilités) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
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Mon, 07/06/2004 14:15 |
Laurent Saloff-Coste (Cornell University) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| The convergence to stationarity of many finite ergodic Markov chains presents a sharp cut-off: there is a time T such that before time T the chain is far from its equilibrium and, after time T, equilibrium is essentially reached. We will discuss precise definitions of the cut-off phenomenon, examples, and some partial results and conjectures. | |||
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Mon, 07/06/2004 15:45 |
Arnaud de La Pradelle (University of Paris VI, France) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| A version of Lyons theory of rough path calculus which applies to a subclass of rough paths for which more geometric interpretations are valid will be presented. Application will be made to the Brownian and to the (fractional) support theorem. | |||
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Mon, 14/06/2004 14:15 |
Chris Potter (Oxford) |
Stochastic Analysis Seminar |
DH 3rd floor SR |
| Complete stochastic volatility models provide prices and hedges. There are a number of complete models which jointly model an underlying and one or more vanilla options written on it (for example see Lyons, Schonbucher, Babbar and Davis). However, any consistent model describing the volatility of options requires a complex dependence of the volatility of the option on its strike. To date we do not have a clear approach to selecting a model for the volatility of these options | |||
