Seminar Calendar
for Probability Seminar events the next 12 months of Saturday, August 1, 2009.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery. 
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Tuesday, September 1, 2009

Graduate Student Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, September 1, 2009
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Submitted by hpark48.
Organizational meeting

Tuesday, September 15, 2009

Graduate Student Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, September 15, 2009
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Submitted by hpark48.
Hyunchul Park (UIUC Math)
Boundary Harnack principle for subordinated Brownian motions
Abstract: We will discuss Boundary Harnack principle for subordinated Brownian motions and some perturbation of subordinated Brownian motion.

Tuesday, September 29, 2009

Graduate Student Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, September 29, 2009
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Submitted by hpark48.
Richard Sowers (Department of Mathematics, University of Illinois)
Large Deviations
Abstract: We give an outline of how to study rare events in random systems. This is the theory of large deviations. We motivate several of the main theorems in the field (without proof) and indicate how they can be applied.

Tuesday, October 13, 2009

Graduate Student Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, October 13, 2009
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Submitted by hpark48.
Ao Chen (Department of Mathematics, University of Illinois)
Equidistant sampling of Brownian motion and convergence to the Brownian motion.
Abstract: I will talk about discretization of Brownian motion and difference between the extrema of discrete and continuous versions of Brownian motion, using Riemann zeta function and Euler-Maclaurin summation formula, mostly due to the work of Janssen and Leeuwaarden.

Tuesday, October 20, 2009

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, October 20, 2009
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Submitted by pankikim.
Panki Kim   [email] (Seoul National University, UIUC)
The boundary Haranck principle of the independent sum of Brownian motion and symmetric stable process.
Abstract: In this talk, we consider the family of pseudo differential operators $\{\Delta+ b \Delta^{\alpha/2}; b\in [0, 1]\}$ that evolves continuously from $\Delta$ to $\Delta + \Delta^{\alpha/2}$. We establish a uniform boundary Harnack principle with explicit boundary decay rate for nonnegative functions which are harmonic with respect to $\Delta +b = \Delta^{\alpha/2}$ (or equivalently, the sum of a Brownian motion and an independent symmetric $\alpha$-stable process with constant multiple $b^{1/\alpha}$) in $C^{1, 1}$ open sets.

Tuesday, October 27, 2009

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, October 27, 2009
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Submitted by siudeja.
Krzysztof Bogdan (Wroclaw University of Technology)
Heat kernel estimates for the fractional Laplacian
Abstract: I will report a joint work with Tomasz Grzywny and Michal Ryznar from WUT, Poland, on approximate factorization of the heat kernel of the (Dirichlet) fractional Laplacian in Lipschitz domains (the paper is on arXiv).

Wednesday, October 28, 2009

Graduate Student Probability Seminar
2:00 pm   in 347 Altgeld Hall ,  Wednesday, October 28, 2009
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Submitted by hpark48.
Kunwoo Kim (UIUC math)
To Be Announced

Tuesday, November 3, 2009

Graduate Student Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, November 3, 2009
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Submitted by hpark48.
Kunwoo Kim (Department of Mathematics, University of Illinois)
Effect of drift on noise
Abstract: Consider two processes on different time scales. When one process is driven by the other, as the driving process gets faster and faster, we can characterize the asymptotic behavior of the driven process by stochastic averaging. In this talk, we will consider the case where the driving force is the fast switching process and the drift term of the driven process is 'singular'. We will show via martingale problem of Strook and Varadhan that the law of the driven process converge to that of sticky, reflected, or sticky reflected Brownian motion depending on the drift term.

Tuesday, November 17, 2009

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, November 17, 2009
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Submitted by rsong.
Prof. Elton Hsu (Northwestern University)
Volume Growth and Escape Rate of Brownian motion on a Complete Riemannian manifold
Abstract: We show that the question of how fast Brownian motion on a complete Riemannian manifold escapes to infinity can be effectively answered solely based on the volume growth of the manifold. In this talk time reversal of reflecting Brownian motion and volumes of geodesic balls all come together in this problem and give an elegant and often sharp upper bound of the escaping rate solely in terms of the volume growth function without any extra geometric restriction besides geodesic completeness.

Tuesday, December 1, 2009

Graduate Student Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, December 1, 2009
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Submitted by hpark48.
Xiong Lin (UIUC Math)
CIR process with Application in Finance
Abstract: I will first show some basic properties of CIR process, its simulation; and then I will demonstrate two of its application in finance. One of the application is as volatility part of the Heston model, in this case, I will show how to price simple European vanilla options, and I will also show how to simulate Heston model. The other one is as short rate in the short rate model, and the pricing of some simple Asian options on short interest rate.

Tuesday, December 8, 2009

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, December 8, 2009
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Submitted by rsong.
Prof. Dongsheng Wu (University of Alabama in Huntsville)
On local times of anisotropic Gaussian random fields
Abstract: In this talk, we study the joint continuity of local times for a large class of anisotropic Gaussian random fields, establish sharp local and global Holder conditions for the local times under corresponding anisotropic metrics, and apply these results to study sample path properties of the fields. Furthermore, we compare our results with those under Euclidean metric. This talk is based on a joint work with Yimin Xiao.

Tuesday, January 19, 2010

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, January 19, 2010
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Submitted by rsong.
Prof. Mingyu Xu (Chinese Academy of Sciences)
Constraint BSDE and its application
Abstract: Non-linear backward stochastic differential equations (BSDEs in short) were firstly introduced by Pardoux and Peng (\cite{PP1990}, 1990), who proved the existence and uniqueness of the adapted solution, under smooth square integrability assumptions on the coefficient and the terminal condition, and when the coefficient $g(t,\omega ,y,z)$ is Lipschitz in $(y,z)$ uniformly in $(t,\omega )$. From then on, the theory of backward stochastic differential equations (BSDE) has been widely and rapidly developed. And many problems in mathematical finance can be treated as BSDEs. The natural connection between BSDE and partial differential equations (PDE) of parabolic and elliptic types is also important applications. In this talk, we study a new developement of BSDE, BSDE with contraint. The existence and uniqueness results are presented and we will give some application of this kind of BSDE at last.

Thursday, January 21, 2010

Graduate Student Probability Seminar
2:00 pm   in Altgeld Hall 241,  Thursday, January 21, 2010
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Submitted by hpark48.
Organizational meeting

Tuesday, January 26, 2010

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, January 26, 2010
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Submitted by pankikim.
Panki Kim   [email] (Seoul National University, UIUC)
Global Heat Kernel Estimates for Symmetric Jump Processes
Abstract: In this talk, we discuss the behavior of heat kernel for symmetric jump-type process with jumping kernels comparable to radially symmetric function on the Euclidean space. Sharp two-sided heat kernel estimates for both small and large time will be discussed. This is a joint work with Zhen-Qing Chen and Takashi Kumagai.

Tuesday, February 9, 2010

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, February 9, 2010
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Submitted by rsong.
Prof. Bruce Hajek (UIUC ECE)
A Maximal Inequality for Supermartingales
Abstract: A tight upper bound is given involving the maximum of a supermartingale. Specifically, it is shown that if $Y$ is a semimartingale with initial value zero and quadratic variation process $[Y,Y]$ such that $Y + [Y,Y]$ is a supermartingale, then the probability the maximum of $Y$ is greater than or equal to a positive constant $a$ is less than or equal to $1/(1+a).$ The proof is inspired by dynamic programming. Complements and extensions are also given.

Tuesday, March 9, 2010

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, March 9, 2010
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Submitted by rsong.
Prof. Jin Feng (University of Kansas)
To Be Announced

Tuesday, March 30, 2010

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, March 30, 2010
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Submitted by pankikim.
khyejin@ima.umn.edu (Institute for Mathematics and its Applications)
TBA

Tuesday, April 6, 2010

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, April 6, 2010
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Submitted by pankikim.
Hye-Won Kang (University of Minnesota)
The maximal compartment size for space discretization in chemical reaction-diffusion networks
Abstract: Abstract: In this talk, I will discuss how to discretize space for the stochastic spatially-discrete model for chemical reaction-diffusion networks. A system with reaction and diffusion is modeled using a continuous time Markov jump process. Diffusion is described as a jump to the neighboring compartments with proper spatial discretization. Considering stationary mean and variance of each species in each compartment, the maximal compartment size for spatial discretization will be suggested. Then, I will show conditions for the exponential convergence to the uniform solution in the corresponding deterministic spatially-continuous model for chemical reaction-diffusion networks. Conditions obtained from the deterministic model approximate criteria for the maximal compartment size for space discretization from the stochastic model well. This is a joint work with Hans Othmer and Likun Zheng.