Probability Colloquium

The KPZ (Kardar-Parisi-Zhang) equation and its universality class

Speaker(s): 
Herbert Spohn (TU München)
Date: 
Wednesday, April 22, 2015 - 5:15pm
Location: 
Universität Potsdam House 8, Room 0.58

The one-dimensional KPZ equation is a stochastic PDE which describes the dynamics of surface growth. It is one representative of a much larger universality class. I will discuss a few models in this class and explain how they are connected. They all share the common feature to be stochastic integrable.

Minicourse on Adaptive Dynamics

Speaker(s): 
Anton Bovier (Universität Bonn)
Date: 
Monday, March 30, 2015 - 4:00pm to Wednesday, April 1, 2015 - 6:00pm
Location: 
TU Berlin, MA 141 and HU Berlin, BMS Lounge

In this series of lectures I will review some by now classical aspects of stochastic models for adaptive dynamics but also point to some recent and quite exciting developments that have been triggered by interactions with oncologists. Stochastic particle models for adaptive dynamics have been proposed by Diekmann and Law and further pushed by Ferrière, Méléard, Champagnat, and others.

Minicourse on Modelisations of the tumor growth

Speaker(s): 
Pierre Vallois (Université de Lorraine, Nancy)
Date: 
Monday, March 2, 2015 - 4:00pm to Wednesday, March 4, 2015 - 12:00pm
Location: 
Universität Potsdam, TU Berlin

The goal of the course is to present two possible modelisations of the tumor growth. The first one is based on Markov chains and the second one makes use of a diffusion process, solution of a stochastic differential equation.

Linear quadratic optimal control: from deterministic to stochastic

Speaker(s): 
Shanjian Tang (Fudan University)
Date: 
Wednesday, February 4, 2015 - 6:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

Richard Kalman's work on linear quadratic optimal control theory for ordinary differential equations is a milestone in the developments of deterministic optimal control theory. Its extension to stochastic differential equations is interesting both in theory and application, and has attracted a lot of attentions since early sixties in the last century. In this talk, I shall review some of these studies, expose some mathematical difficulties therein, and also give some unsolved problems.

A weak law of large numbers for a limit order book model with fully state dependent order dynamics

Speaker(s): 
Dörte Kreher (HU Berlin)
Date: 
Wednesday, February 4, 2015 - 5:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

In this talk we study a one-sided limit order book (LOB) model, in which the order dynamics depend on both, the current best bid price and the current volume density function. For the joint dynamics of the best bid price and the standing buy volume density we derive a weak law of large numbers, which states that the LOB model converges to a continuous-time limit when the size of an individual order as well as the tick size tend to zero and the order arrival rate tends to infinity.

Dependence Uncertainty, Fréchet-Bounds and Robust Option Pricing

Speaker(s): 
Thibaut Lux (TU Berlin)
Date: 
Wednesday, January 21, 2015 - 5:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

We consider the problem of finding arbitrage bounds for option prices of multi-asset options (i.e. options on multiple underlyings) in the case when only partial information of the assets' probability distribution is available. We focus on the case in which the one-dimensional marginal distribution of each individual asset is known but only partial information of the dependence structure between the assets is available. This is in the literature often referred to as dependence uncertainty. The problem has been extensively studied in two-asset case for which solutions were given by P.

The non-zero velocity regime of a random walk in random environment at low disorder

Speaker(s): 
Alejandro Ramirez (Pontificia Universidad Católica de Chile)
Date: 
Wednesday, January 7, 2015 - 6:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

We consider a random walk whose jump probabilities are i.i.d. perturbations of those of the simple symmetric random walk. This walk can exhibit a variety of behaviors, ranging from recurrent to transient regimes with zero or non-zero velocity. Under the condition that the average jump after one step (local drift) is not too small, it was proved by Sznitman, that the random walk has a non-zero velocity. Using a renormalization approach, we establish that under the same condition, the velocity is asymptotically equal to the local drift as the strength of the perturbation vanishes.

On dynamic portfolio choice with price impact

Speaker(s): 
Moritz Voss (TU Berlin)
Date: 
Wednesday, January 7, 2015 - 5:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

We propose a variant of the limit order book model by Obizhaeva and Wang (2013) which allows for both selling and buying stock. Specifically, our price impact model determines bid- and ask-prices via a coupled system of controlled diffusions, allowing us to retain the possibility to specify market depth, tightness and resilience. We discuss the problem of optimal investment in this model.

Stable Processes: Absolute continuity and singularity under a purely discontinuous Girsanov transform

Speaker(s): 
Rene Schilling (TU Dresden)
Date: 
Wednesday, December 10, 2014 - 6:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

We are interested in mutual absolute continuity and singularity of probability measures on the path space which are induced by an isotropic stable Lévy process and the purely discontinuous Girsanov transform of this process. We also look at the problem of finiteness of the relative entropy of these measures. An important tool is the question under which circumstances the a.s. finiteness of an additive functional at infinity implies the finiteness of its expectation.
(Joint work with Zoran Vondracek, Zagreb)

What the frequency spectrum in the infinite-sites model can teach us about the underlying coalescent

Speaker(s): 
Eugenio Buzzoni (TU Berlin)
Date: 
Wednesday, December 10, 2014 - 5:00pm
Location: 
HU Berlin, Rudower Chaussee 25, 12489 Berlin, Room 1.115

The site frequency spectrum (SFS) is an important and well-studied summary statistic of population genetic data, capturing aspects of the underlying genealogical tree. For example, a recent increase in population size leads to an excess of `singletons' in the spectrum relatively to a population in equilibrium. In this talk I will present basic population genetic models and properties of the SFS that they produce. The question whether the SFS contains enough information to recover the full demographic history of a population has recently been investigated.

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