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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： On the dimension of limit sets on the real projective plane via stationary measures
实射影平面 极限集 维数 平稳测度
2023/11/29
I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the dimension of limit sets on the real projective plane via stationary measures
实射 影平面 极限集 维数 平稳测度
2023/11/15
I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements I: Large deviation principle of occupation measures
随机交错 大偏差 占用措施 大偏差原则
2023/5/10
In this lecture, I will talk about the large deviation problems in random interlacements, in particular the LDP of the occupation measure, and discuss its relations to sharp asymptotic probabilities o...
From Smile Asymptotics to Market Risk Measures
dynamic convex risk measures volatility skew stochastic volatility models indifference pricing backward stochastic differential equations
2011/10/9
Abstract: The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices...
Free Completely Random Measures
Bayesian non parametrics Bercovici-Pata bijection free completely random measures free infinite divisibility free probability
2011/9/15
Abstract: Free probability is a noncommutative probability theory introduced by Voiculescu where the concept of independence of classical probability is replaced by the concept of freeness. An importa...
Developments in perfect simulation for Gibbs measures
Perfect Simulation Stochastic Order Gibbs Measures
2011/8/30
Abstract: This paper deals with the problem of perfect sampling from a Gibbs measure with infinite range interactions. We present some sufficient conditions for the extinction of processes which are l...
Information theoretic interpretation of frequency domain connectivity measures
Information theoretic interpretation frequency domain connectivity measures
2011/1/17
To provide adequate multivariate measures of information flow between neural structures, modified expressions of Partial Directed Coherence (PDC) and Directed Transfer Function (DTF), two popular mult...
Foliated stochastic calculus: Harmonic measures
Foliation diffusion process stochastic calculus
2011/2/24
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foli-ation.
Finitely additive equivalent martingale measures
Arbitrage de Finetti’s coherence principle equivalent martin-gale measure
2011/1/21
Let L be a linear space of real bounded random variables on the probability space ( ,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L.
A Ham Sandwich Analogue for Quaternionic Measures and Finite Subgroups of S^3
Ham Sandwich Analogue Quaternionic Measures Finite Subgroups of S^3
2010/12/14
A “ham sandwich” theorem is established for n quater-nionic Borel measures on quaternionic space Hn. For each finite sub-group G of S3.
Kerov's central limit theorem for Schur-Weyl measures of parameter 1/2
Kerov's central limit theorem Schur-Weyl measures parameter 1/2
2010/12/9
In this article, we show that Kerov’s central limit theorem related to the fluctuations of
Young diagrams under the Plancherel measure extends to the case of Schur-Weyl measures, which are the probab...
In this paper we study the asymptotic behaviour of the escape rate of a Gibbs measure supported on a conformal repeller through a small hole. There are additional applications to the convergence of Ha...
A New Factorization Property of the Selfdecomposable Probability Measures
Selfdecomposable s-selfdecomposable background driving L´ evy process class U class L factorization property
2010/12/8
We prove that the convolution of a selfdecomposable dis-tribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable.