Stochastic Analysis Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
Today
14:15
PANPAN REN
Abstract

By using Malliavin calculus, Bismut type formulas are established for the Lions derivative of , where  0,  is a bounded measurable function,  and  solves a distribution dependent SDE with initial distribution . As applications, explicit estimates are derived for the Lions derivative and the total variational distance between distributions of   solutions with different initial data. Both degenerate and non-degenerate situations are considered. Due to the lack of the semi-group property  and the invalidity of the formula =  , essential difficulties are overcome in the study.

Joint work with Professor Feng-Yu Wang

  • Stochastic Analysis Seminar
Today
15:45
MICHAEL McAULEY
Abstract

The physics literature has for a long time posited a connection between the geometry of continuous random fields and discrete percolation models. Specifically the excursion sets of continuous fields are considered to be analogous to the open connected clusters of discrete models. Recent work has begun to formalise this relationship; many of the classic results of percolation (phase transition, RSW estimates etc) have been proven in the setting of smooth Gaussian fields. In the first part of this talk I will summarise these results. In the second I will focus on the number of excursion set components of Gaussian fields in large domains and discuss new results on the mean and variance of this quantity.

 

  • Stochastic Analysis Seminar
29 October 2018
14:15
FABIAN ANDSEM HARANG
Abstract

In this seminar we will look at an extension of the well known sewing lemma from rough path theory to fields on [0; 1]k. We will first introduce a framework suitable to study such fields, and then find a criterion for convergence of multiple Riemann type sums of a class of abstract integrands. A simple application of this extension is construct the Young integral for fields.Furthermore, we will discuss the use of this theorem to study integration of fields of lower regularity by using ideas familiar from rough path theory. Moreover, we will discuss difficulties we face by looking at “multi-parameter ODE's” both from an existence and uniqueness point of view.

 

  • Stochastic Analysis Seminar
29 October 2018
15:45
HUY TRAN
Abstract

SLE curves are an important family of random curves in the plane. They share many similarites with solutions of SDE (in particular, with Brownian motion). Any quesion asked for the latter can be asked for the former. Inspired by that, Yizheng Yuan and I investigate the support for SLE curves. In this talk, I will explain our theorem with more motivation and idea. 

 

 

  • Stochastic Analysis Seminar
5 November 2018
14:15
Abstract

I will consider cost minimizing stopping time solutions to Skorokhod embedding problems, which deal with transporting a source probability measure to a given target measure through a stopped Brownian process. A PDE (free boundary problem) approach is used to address the problem in general dimensions with space-time inhomogeneous costs given by Lagrangian integrals along the paths.  An Eulerian---mass flow---formulation of the problem is introduced. Its dual is given by Hamilton-Jacobi-Bellman type variational inequalities.  Our key result is the existence (in a Sobolev class) of optimizers for this new dual problem, which in turn determines a free boundary, where the optimal Skorokhod transport drops the mass in space-time. This complements and provides a constructive PDE alternative to recent results of Beiglb\"ock, Cox, and Huesmann, and is a first step towards developing a general optimal mass transport theory involving mean field interactions and noise.

  • Stochastic Analysis Seminar
5 November 2018
15:45
IAN MELBOURNE
Abstract

The classical Lorentz gas model introduced by Lorentz in 1905, studied further by Sinai in the 1960s, provides a rich source of examples of chaotic dynamical systems with strong stochastic properties (despite being entirely deterministic).  Central limit theorems and convergence to Brownian motion are well understood, both with standard n^{1/2} and nonstandard (n log n)^{1/2} diffusion rates.

In joint work with Paulo Varandas, we discuss examples with diffusion rate n^{1/a}, 1<a<2, and prove convergence to an a-stable Levy process.  This includes to the best of our knowledge the first natural examples where the M_2 Skorokhod topology is the appropriate one.



 

  • Stochastic Analysis Seminar
12 November 2018
14:15
GUISEPPE CANNIZZARO
Abstract

In the context of randomly fluctuating surfaces in (1+1)-dimensions two Universality Classes have generally been considered, the Kardar-Parisi-Zhang and the Edwards-Wilkinson. Models within these classes exhibit universal fluctuations under 1:2:3 and 1:2:4 scaling respectively. Starting from a modification of the classical Ballistic Deposition model we will show that this picture is not exhaustive and another Universality Class, whose scaling exponents are 1:1:2, has to be taken into account. We will describe how it arises, briefly discuss its connections to KPZ and introduce a new stochastic process, the Brownian Castle, deeply connected to the Brownian Web, which should capture the large-scale behaviour of models within this Class. 

 

  • Stochastic Analysis Seminar
12 November 2018
15:45
ANTOINE LEJAY
Abstract

Solutions to Rough Differential Equations (RDE) may be constructed by several means. Beyond the fixed point argument, several approaches rely on using approximations of solutions over short times (Davie, Friz & Victoir, Bailleul, ...). In this talk, we present a generic, unifying framework to consider approximations of flows, called almost flows, and flows through the non-linear sewing lemma. This framework unifies the approaches mentioned above and decouples the analytical part from the algebraic part (manipulation of iterated integrals) when studying RDE. Beyond this, flows are objects with their own properties.New results, such as existence of measurable flows when several solutions of the corresponding RDE exist, will also be presented.

From a joint work with Antoine Brault (U. Toulouse III, France).

 

  • Stochastic Analysis Seminar
19 November 2018
14:15
LUKAS GONON
Abstract

We consider the problem of optimally hedging a portfolio of derivatives in a scenario based discrete-time market with transaction costs. Risk-preferences are specified in terms of a convex risk-measure. Such a framework has suffered from numerical intractability up until recently, but this has changed thanks to technological advances: using hedging strategies built from neural networks and machine learning optimization techniques, optimal hedging strategies can be approximated efficiently, as shown by the numerical study and some theoretical results presented in this talk (based on joint work with Hans Bühler, Ben Wood and Josef Teichmann). We also discuss alternative choices of architectures (based on joint work with Juan-Pablo Ortega).

  • Stochastic Analysis Seminar
19 November 2018
15:45
ALEXEY KOREPANOV
Abstract

I will talk about R^n valued random processes driven by a "noise", which is generated by a deterministic dynamical system, randomness coming from the choice of the initial condition.

Such processes were considered by D.Kelly and I.Melbourne.I will present our joint work with I.Chevyrev, P.Friz, I.Melbourne and H.Zhang, where we consider the noise with long term memory. We prove convergence to solution of a stochastic differential equation which is, depending on the noise, driven by either a Brownian motion (optimizing the assumptions of Kelly-Melbourne) or a Lévy process.Our work is made possible by recent progress in rough path theory for càdlàg paths in p-variation topology.

 

  • Stochastic Analysis Seminar
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