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Shige peng speaker 2014

We consider a typical situation in which probability model itself has non-negligible cumulated uncertainty. A new concept of nonlinear expectation and the corresponding non-linear distributions has been systematically investigated: cumulated nonlinear i. The continuous time uncertainty accumulation derives a nonlinear Brownian motion as well as the corresponding OU-process driven by this nonlinear Brownian motion which converges to a nonlinear invariant measure of Gaussian type. The related stochastic calculus provides us a powerful tools to introduce time-space derivatives for functional of paths. The corresponding Feynman-Kac formula for gives one to one correspondence between fully nonlinear parabolic partial differential equations and backward stochastic differential equations driven by the nonlinear Brownian motion. Speakers Shige Peng.


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The idea is to bring together people from around Oxford who are interested in probability and related areas for a one day meeting. We hope to make it a regular event with broad coverage of the topic. The first meeting was on 9th December The second meeting will be March The speakers and will be:. All talks will be in Mathematical Institute, lecture rooms L2 and L4. The seminar room C4 is reserved for discussions. You can download the program in PDF.

Bakry Toulouse, France : Brownian motion on symmetric matrices constructed over Clifford algebras. Abstract:Clifford algebras are associative algebraic structures living in spaces with dimension.

With the help of the algebra structure, one may construct real symmetric matrices with dimension on which live natural diffusion processes such as Brownian motion or Ornstein-Uhlenbeck operator.

It turns out that the spectral measures of these matrices are again diffusion processes, and that the structure of these processes reflects the algebraic structure of the algebra. We thus recover the well-known Bott's periodicity property of the Clifford algebra.

We shall also consider briefly octonionic structures where the situation is much more delicate. In a celebrated paper, Smirnov proved that critical site-percolation on the regular triangular lattice has a non-trivial, conformally invariant scaling limit and that this can be used to derive for instance the value of critical exponents.

The argument is unfortunately very specific to this particular lattice, and so far has not been generalized to any other natural case - in particular, percolation on is much beyond reach of current methods.

I will present one direction in which the proof can be extended into a non-trivial class of models that somehow interpolate between the triangular lattice and general planar cases. Abstract:The formal series of iterated path integrals has been an object of significant interest in topology, algebra and more recently, rough path theory. The non-commutative multiplication makes it difficult to prove precise facts about the series.

We shall discuss two of these open problems. The first is "surjectiveness" problem, that is, which tensor elements can be realised as the series of iterated integrals of some paths. The second is "injectiveness", that is what information about a path can one recovers from its iterated integrals. It turns out that some results on these two problems can be obtained using the concept of winding number. In our work, after a general discussion of derivatives of functions of probability measures and the second order Taylor expansion for such functions, we study a flow associated with stochastic differential equations SDEs of mean-field type, i.

This discussion allows to derive a non local PDE which unique solution is described with the help of the mean-field SDE. Tom Cass Imperial College : Rough path analysis: a survey and some illustrative applications. Abstract: We review the theory of rough path analysis and rough differential equation. We then illustrate the usefulness of this approach by analysing in detail some recent applications in stochastic analysis.

Zengjing Chen Shandong University, Jinan : Necessary and sufficient conditions for the law of large numbers for capacities. Abstract: In this paper, we investigate strong laws of large numbers for capacities under weaken conditions.

We obtain two results: One is a sufficient and almost necessary condition under which any cluster point of empirical average lies, with probability capacity one, between upper and lower Choquet integrations; The other is a sufficient and almost necessary condition under which the interval between upper and lower Choquet integrations is the unique smallest interval in which any cluster point of empirical average lies with probability capacity one.

Furthermore, we study some examples to explain the application about the strong laws of large numbers for capacities. Keywords: Capacity, Choquet expectation, independent, law of large numbers, sub-linear expectation. David Croydon Warwick, UK : Quenched invariance principles for random walks and random divergence forms in random media with a boundary. Abstract: I will discuss recent joint work with Zhen-Qing Chen University of Washington and Takashi Kumagai Kyoto University that establishes, via a Dirichlet form extension theorem and making full use of two-sided heat kernel estimates, quenched invariance principles for random walks and random divergence forms in random media with a boundary.

In particular, our results demonstrate that the random walk on a supercritical percolation cluster or amongst random conductances bounded uniformly from below in a half-space, quarter-space, etc. I will also discuss a similar result for the random conductance model in a box, which allows improvements to be made to existing asymptotic estimates for the relevant mixing time.

Furthermore, in the uniformly elliptic case, I will present quenched invariance principles for domains with more general boundaries. Abstract: If one starts with a uniformly ergodic Markov chain on countable states, what sort of perturbation can one make to the transition rates and still retain uniform ergodicity?

In this talk, we will consider a class of perturbations that can be simply described, where a uniform estimate on convergence to an ergodic distribution can be obtained. Abstract: In this talk, we present the boundedness of the inverse of Malliavin Matrix for Degenerate stochastic differential equations with some new conditions, which is equivalent to the Hoermander conditions as the coefficients are smooth. Also, the gradient estimates for the semigroup is given. Abstract:We will give a survey on recent development of stochastic differential equations, as well as its connection with hydrodynamics.

We establish the existence of a unique bounded solution to an infinite horizon discounted BSDE. We then use the vanishing discount approach together with coupling techniques to obtain a Markovian solution to the EBSDE.

We also prove uniqueness under certain growth conditions. Applications are then given, in particular to risk-averse ergodic optimal control and power plant evaluation under uncertainty. The main strategy is a strengthened Le Jan-Qian approximation scheme and the Malliavin calculus. In the end I will also give some remarks on possible ways to attack the deterministic uniqueness of signature problem for geometric p-rough paths.

Elton P. Abstract: Levy showed that the total time that a standard Brownian motion stays positive up to time 1 obeys the arcsine law. We will discuss the deviation of this law for a Brownian motion on a Riemannian manifold near a smooth hypersurface.

The deviation has the order of the square root of the total time and is proportional to the mean curvature of the hypersurface. Its explicit form depends on the local time of the transversal Brownian motion properly scaled. Abstract: We will introduce the noisy integrate-and-fire model used to describe the evolution of the electrical potential across a single neuron, before considering a network of such neurons that interact through an instantaneous mean-field threshold dynamic when the potential of a single neuron reaches a threshold, it is reset while all the others receive an instantaneous kick.

We show that in the limit when the size of the network becomes infinite, the resulting equation may exhibit a blow-up phenomenon under certain conditions, when a large proportion of neurons all emit a spike at the same time which has been linked with epilepsy.

We moreover show that the particle system does indeed exhibit propagation of chaos, and propose a new way to give sense to a solution after a blow-up. This is based on joint research with F. Delarue Nice , E. Rubenthaler Nice. Abstract: In this talk we will study a new special mean-field problem in a purely probabilistic method, to characterize its limit which is the solution of mean-field backward stochastic differential equations BSDEs with reflections, and we will give the probabilistic interpretation of the nonlinear and nonlocal partial differential equations with the obstacles by the solutions of reflected mean-field BSDEs.

Furthermore, we will study the optimal control problems of such reflected mean-field BSDEs. Finally, we will show that the value function which our reflected MFBSDE is coupled with is the unique viscosity solution of the related nonlocal parabolic partial differential equation with obstacle.

Abstract: The process of distribution functions of a one-dimensional super-Levy process is characterized as the pathwise unique solution of a stochastic integral equation driven by Gaussian and Poisson time-space noises, which generalizes the recent work of Xiong AOP, on super-Brownian motion. To prove the pathwise uniqueness of the solution we establish a connection of the stochastic integral equation with some backward doubly stochastic equation with jumps.

This is based on a joint work with Hui He and Xu Yang. Abstract: In the study of open quantum systems, memory effects are usually ignored, and this leads to dynamical semi-groups and Markovian dynamics. However, in practice, non-Markovian dynamics is the rule rather than exception. With the recent emergence of quantum information theory, there is a flurry of investigations of quantum non-Markovian dynamics.

In this talk, we first review several significant measures for non-Markovianity, such as deviation from divisibility, information exchange between a system and its environment, or entanglement with the environment.

Then by exploiting the correlations flow between a system and an arbitrary ancillary, we study a considerably intuitive measure for quantum non-Markovianity by use of correlations as quantified by quantum mutual information rather than entanglement. The measure captures quite directly and deeply the characteristics of quantum non-Markovianity from the perspective of information.

A simplified version based on Jamiolkowski-Choi isomorphism which encodes operations via bipartite states and does not involve any optimization is also investigated. Abstract: Consider the following extension of the Erdos-Renyi random graph process; in a graph on vertices, each edge arrives at rate 1, but also each vertex is struck by lightning at rate , in which case all the edges in its connected component are removed. Such a "mean-field forest fire" model was introduced by Rath and Toth.

For appropriate ranges of , the model exhibits "self-organised criticality". We investigate scaling limits, involving a multiplicative coalescent with an added "deletion" mechanism. I'll mention a few other related models, including epidemic models and "frozen percolation" processes. Joint work with Balazs Rath. Abstract: MCMC methods are popular algorithms to sample from a given probability measure. Roughly, these algorithms are based on constructing an ergodic Markov Chain which has the target measure as unique invariant measure.

We describe a new MCMC method optimized for the sampling of probability measures defined on infinite dimensional Hilbert spaces and having a density with respect to a Gaussian; such measures arise in the Bayesian approach to inverse problems, and in conditioned diffusions.

The method we introduce is based on Hamiltonian mechanics as well, and it is tailored to incorporate the two described design principles. This is a joint work with N. Pillai, F. Pinski and A.

Abstract: SLE curves are introduced by Oded Schramm as the candidate of the scaling limit of discrete models. In this talk, we first describe basic properties of SLE curves and their relation with discrete models. Then we summarize the Hausdorff dimension results related to SLE curves, in particular the new results about the dimension of cut points and double points. Third we introduce Imaginary Geometry, and from there give the idea of the proof of the dimension results.

Abstract: This talk is concerned with backward stochastic differential equations BSDEs coupled by a finite-state Markov chains. This kind of BSDEs has wide applications in optimal control theory and mathematical finance. The underlying Markov chain is assumed to have a two-time scale structure. Namely, the states of the Markov chain can be divided into a number of groups so that the chain jumps rapidly within a group and slowly between the groups.

In this talk, we illustrate two convergence results as the fast jump rate goes to infinity, which can be used to reduce the complexity of the original problem.

This method is also referred to as singular perturbation. The limit process is a solution of aggregated BSDEs. The results are applied to a set of partial differential equations and used to validate their convergence to the corresponding limit system. The second one is the optimal switching problem for regime-switching model with two-time-scale Markov chains.


Fields-China Joint Industrial Problem Solving Workshop in Finance

Stephen Smale born July 15, is an American mathematician whose research concerns topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in and spent more than three decades on the mathematics faculty of the University of California, Berkeley. In , Smale was awarded the Wolf Prize in mathematics. Smale began his career as an instructor at the college at the University of Chicago.

Invited Speakers of ICIAM About ICIAM. The ICIAM newsletter was created to express the interests.

Numerical Study on G-Expectation


Keynote Speaker: Ma Zhiming. Speaker Introduction: Ma Zhiming, mathematician and academician of the Chinese Academy of Sciences, has made enormous contributions in probability theory and stochastic analysis, and significant breakthroughs in studying the corresponding relation between Dirichlet form and Markov process. In , he was elected as an academician of the Chinese Academy of Sciences; in , he was elected as an academician of the Third World Academy of Sciences; in , he was elected as a fellow of the Institute of Mathematical Statistics IMS. He served as chairman of the Organizing Committee of the International Congress of Mathematicians in Beijing; member and vice chairman of the Executive Committee of International Mathematical Union; president of the 8th and 10th Chinese Mathematical Society; president of the China Probabilistic and Statistical Association ; member of the National Textbook Committee in ; and he is currently the dean of the School of Mathematical Sciences, USTC. Host: Peng Shige, professor of the School of Mathematics. Time: , June 10, Monday. Hosted by: School of Mathematics, Shandong University. Title: Probabilistic and Statistical Methods of Big Data Analysis Keynote Speaker: Ma Zhiming Speaker Introduction: Ma Zhiming, mathematician and academician of the Chinese Academy of Sciences, has made enormous contributions in probability theory and stochastic analysis, and significant breakthroughs in studying the corresponding relation between Dirichlet form and Markov process.

Peng Shige

shige peng speaker 2014

The interaction between industry and academia has many potential benefits for both. Academics learn about interesting potential research problems and find application for their existing tools. Industries get access to some of the most experienced mathematical modellers and problem-solvers on the continent. At the end of the week, the academic experts make a presentation consisting of the problem restatement and their solution. This is a summary of results; the teams also prepare reports for the industrial sponsors.

The idea is to bring together people from around Oxford who are interested in probability and related areas for a one day meeting.

Seminar Event


A major challenge in many modern economic, epidemiological, ecological and biological questions is to understand the randomness in the network structure of the entities they study. Although analysis of data on networks goes back to at least the s, the importance of statistical network modelling for many areas of substantial science has become more pronounced since the turn of the century. This Committee on Statistical Network Science CSNS will focus on promoting and fostering research in statistical and probabilistic network analysis, in the wider sense. This remit includes graphical models, random graph models as well complex functional network models. The Medal is in honour of Willem van Zwet, who served Bernoulli Society and its aims in many special ways.

Past Colloquia

Geom, Math. Hugh C. This Roundtable will bring together representatives from all the BC research universities, government and industry to discuss research priorities and explore various mechanisms to promote collaborative engagement and research. General Hardy-type inequalities on manifolds. Singularities in Lagrangian Mean Curvature Flow. High Rayleigh number convection in porous media. Set Theory: the last 50 years.

Peng Shige (born December 8, ) is a Chinese mathematician noted for his Chen was elected Member of the Academy of Europe in and Fellow of The.

Events Archive

Title: Conference on Stochastic Analysis, Stochastic Dynamical Systems and Stochastic Finance Abstract: In recent years, fundamental advances have been made in different areas of stochastics — from stochastic partial differential equations, ergodic theory to manifold valued stochastic differential equations as well as non-dominated models and transport methods in financial mathematics. The School of Mathematical Sciences takes this opportunity to bring together those working on different areas of research related to stochastics to exchange on common issues, their respective approaches, new results and new research directions. Alongside the presentation of each speaker, this conference also intends to facilitate research discussions and interactions in a stimulating and convivial atmosphere. Attendance is open to any interested participants up to capacity.

Activities


Skip to main content. Feb 7 - pm. Math Department: Faculty Meeting. Feb 1 - pm to pm.

Program News.

International Conference on Stochastic Analysis and its Applications

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1st BYO Workshop in Probability and Finance

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  1. Akker

    I did not understand the connection of the title with the text

  2. Clarke

    Today I read a lot on this subject.

  3. Sol

    Dear blog author, are you by any chance from Moscow?