Forthcoming Seminars › Seminar Series

Stochastic Analysis Seminar

Mon, 19/01/2009
14:15 		Professor Sandy Davie (Edinburgh) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Existence of unique solutions for SDEs for individual driving paths.
Existence and uniqueness theorems for (vector) stochastic differential equations dx=a(t,x)dt+b(t,x)dW are usually formulated at the level of stochastic processes. If one asks for such a result for an individual driving Brownian path W then there is a difficulty of interpretation.One solution to this is to use rough path theory, and in this context a uniqueness theorem can be proved (for a.e. W) for dx=b(x)dW if b has Holder continuous derivative. Another variant with a natural interpretation is dx=a(t,x)dt+dW where, if a is bounded Borel, uniqueness can be shown for a.e. W. The talk will explore the extent to which these two approaches can be combined.
Mon, 19/01/2009
15:45 		Dr Daniel Levin (Oxford) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
A new combinatorial method for calculating the moments of Lévy area
We present a new way to compute the moments of the Lévy area of a two-dimensional Brownian motion. This is a classical problem of great importance, originally solved by Lévy. Our approach uses iterated integrals and combinatorial arguments involving the shuffle product (joint paper with Mark Wildon, Swansea). 
Thu, 22/01/2009
14:15 		Bruno Bouchard (Paris, Dauphine) Stochastic Analysis Seminar Add to calendar DH 1st floor SR
Optimal Control Under Stochastic Target Constraints
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Mon, 26/01/2009
14:15 		Dr Z Qian (Oxford) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Stochastic Navier-Stokes equations
Mon, 26/01/2009
15:45 		Dr Jon Warren (University of Warwick) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
The TASEP with deterministic leading particle
Mon, 02/02/2009
14:15 		Professor Hans Föllmer Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Preferences and implicit risk measures
We discuss some connections between various notions of rationality in the face of uncertainty and the theory of convex risk measures, both in a static and a dynamic setting.
Mon, 02/02/2009
15:45 		Professor Hong-Quan Li (Fudan University) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Gradient estimate for the heat semi-group and heat estimates on H-type groups
In this talk, we give the asymptotics estimates for the heat kernel and its gradient estimates on H-type groups. Moreover, we get gradient estimates for the heat semi-group.
Mon, 09/02/2009
14:15 		Dr Jan Obloj (Oxford) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Azema-Yor processes: three characterisation theorems
We study the class of Azema-Yor processes which are of the form F(M_t)-f(M_t)(X_t-M_t), where F'=f, X_t is a semimartingale with no positive jumps and M_t is its running maximum. We show that these processes arise as unique strong solutions to the Bachelier SDE which we also show is equivalent to the DrawDown SDE. The proofs are greatly simplified thanks to (algebraic) group property of the set of AY processes indexed by functions. We then restrict our attention to the case when X is a martingale. It turns out that the AY martingales are the only local martingales of the form H(X_t,M_t) for a Borel function H. Furthermore, they can also be characterised by their optimal properties: all uniformly integrable martingales whose maximum dominates a given target are dominated by an AY martingale in the concave ordering of terminal values. We mention how these results find direct applications in portfolio optimisation/insurance theory. Joint work with Laurent Cararro and Nicole El Karoui
Mon, 09/02/2009
15:45 		Dr Nikolaos Zygouras (Warwick) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Pinning-depinning transition in Random Polymers
Random polymers are used to model various physical ( Ising inter- faces, wetting, etc.) and biological ( DNA denaturation, etc.) phenomena They are modeled as a one dimensional random walk (Xn), with excursion length distribution P(E1 = n) = (n)=nc, c > 1, and (n) a slowly varying function. The polymer gets a random reward, whenever it visits or crosses an interface. The random rewards are realised as a sequence of i.i.d. variables (Vn). Depending on the relation be- tween the mean value of the disorder Vn and the temperature, the polymer might prefer to stick on the interface (pinning) or undergo a long excursion away from it (depinning). In this talk we will review some aspects of random polymer models. We will also discuss in more detail the pinning-depinning transition of the 'Pinning' model and also its relation to other directed polymer models
Mon, 16/02/2009
14:15 		Professor Xunyu Zhou (Oxford) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Non Expected Utility Maximisation
Mon, 16/02/2009
15:45 		Dr Andrew Wade (Bristol) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Stochastic billiards in unbounded planar domains
 Motivated by ideal gas models in the low density regime, we study a randomly reflecting particle travelling at constant speed in an unbounded domain in the plane with boundary satisfying a polynomial growth condition The growth rate of the domain, together with the reflection distribution, determine the asymptotic behaviour of the process. We give results on recurrence vs. transience, and on almost-sure-bounds for the particle including the rate of escape in the transient case. The proofs exploit a surprising relationship with Lamperti's problem of a process on the half-line with asymptotically zero drift. This is joint work with Mikhail Menshikov and Marina Vachkovskaia.
Mon, 23/02/2009
14:15 		Dr Sergei Zuev (University of Strathclyde) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Stochastic geometry and telecommunications modelling
Stochastic geometry gradually becomes a necessary theoretical tool to model and analyse modern telecommunication systems, very much the same way the queuing theory revolutionised studying the circuit switched telephony in the last century. The reason for this is that the spatial structure of most contemporary networks plays crucial role in their functioning and thus it has to be properly accounted for when doing their performance evaluation, optimisation or deciding the best evolution scenarios.  The talk will present some stochastic geometry models and tools currently used in studying modern telecommunications.  We outline specifics of wired, wireless fixed and ad-hoc systems and show how the stochastic geometry modelling helps in their analysis  and optimisation.
Mon, 23/02/2009
15:45 		Dr Victor Kleptsyn (Université de Rennes) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Random walks on transversally confomal foliations (on a joint work with B.Deroin).
Given a foliation of a compact manifold, leaves of which are equipped with a Riemannian metric, one can consider the associated "leafwise" Brownian motion, and study its asymptotic properties (such as asymptotic distribution, behaviour of holonomy maps, etc.). Lucy Garnet studied such measures, introducing the notion of a harmonic measure – stationary measure of this process; the name "harmonic" comes from the fact that a measure is stationary if and only if with respect to it integral of every leafwise Laplacian of a smooth function equals zero (so, the measure is "harmonic" in the sense of distributions). It turns out that for a transversally conformal foliation, unless it possesses a transversally invariant measure (which is a rather rare case), the associated random dynamics can be described rather precisely. Namely, for every minimal set in the foliation there exists a unique harmonic measure supported on it – and this gives all the possible ergodic harmonic measures (in particular, there is a finite number of them, and they are always supported on the minimal sets). Also, the holonomy maps turn out to be (with probability one) exponentially contracting – so, the Lyapunov exponent of the dynamics is negative. Finally, for any initial point almost every path tends to one of the minimal sets and is asymptotically distributed with respect to the corresponding harmonic measure – and the functions defining the probabilities of tending to different sets form a base in the space of continuous leafwise harmonic functions. An interesting effect that is a corollary of this consideration is that for transversally conformal foliations the number of the ergodic harmonic measures does not depend on the choice of Riemannian metric on the leaves. This fails for non-transversally conformal foliations: there is an example, recently constructed in a joint with S.Petite (following B.Deroin's technique).
Mon, 02/03/2009
14:15 		Professor Marta Sanz Solé (Universitat de Barcelona) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Some criteria for hitting probabilities. Application to systems of stochastic wave equation with additive noise
We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k≥1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and coloured in space.
Mon, 02/03/2009
15:45 		Professor Yue-Yun Hu (Université Paris XIII) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Minimal position in branching random walk
This talk is based on a joint work with Zhan Shi: We establish a second-order almost sure limit theorem for the minimal position in a one-dimensional super-critical branching random walk, and also prove a martingale convergence theorem which answers a question of Biggins and Kyprianou (2005). Our method applies furthermore to the study of directed polymers on a disordered tree. In particular, we give a rigorous proof of a phase transition phenomenon for the partition function (from the point of view of convergence in probability), already described by Derrida and Spohn (1988). Surprisingly, this phase transition phenomenon disappears in the sense of upper almost sure limits.
Mon, 09/03/2009
14:15 		Jean Picard (Universite Blaise Pascal) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
A tree approach to the analysis of real paths with unbounded variation
Mon, 09/03/2009
15:45 		Dr David Croydon (University of Warwick) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Random walks on random graphs and trees
I will discuss scaling properties of simple random walks on various random graphs, including those generated by random walk paths, branching processes and branching random walk, and briefly describe how attempting to understand the random walk on a critical percolation cluster provides some motivation for this work.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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