Brownian motion

Monday, June 11, 2018 - 1:30pm - 2:00pm
Philip Ernst (Rice University)
Suppose you have one unit of stock, currently worth 1, which you must sell before time $T$. The Optional Sampling Theorem tells us that whatever stopping time we choose to sell, the expected discounted value we get when we sell will be 1. Suppose however that we are able to see $a$ units of time into the future, and base our stopping rule on that; we should be able to do better than expected value 1. But how much better can we do? And how would we exploit the additional information?
Monday, June 11, 2018 - 2:00pm - 2:30pm
David Prager (Anderson University)
Stock loans involve two parties: a borrower and a lender. The borrower owns one share of stock and obtains a loan from the lender using the share of stock as collateral. At maturity, the borrower must choose between 1) repaying the lender the principal plus interest to regain the stock and 2) defaulting on the loan and surrendering the stock. Most classical work on stock loan valuation used Brownian motion-based stock models, but recently Markov chain models have gained in popularity.
Thursday, June 14, 2018 - 11:00am - 11:50am
Hailiang Yang (University of Hong Kong)
Motivated by the Guaranteed Minimum Death Benefits in various deferred annuities, we investigate the calculation of
the expected discounted value of a payment at the time of death. The payment depends on the price of a stock at that
time and possibly also on the history of the stock price. If the payment turns out to be the payoff of an option,
we call the contract for the payment a (life) contingent option. Because each time-until-death distribution can be approximated
Thursday, June 25, 2015 - 1:15pm - 2:15pm
Krzysztof Burdzy (University of Washington)
I will present some results on obliquely reflected Brownian motion in fractal domains. Time permitting, I will also discuss discrete approximations of reflected Brownian motion in fractal domains. Joint work with Zhenqing Chen, Donald Marshall and Kavita Ramanan.
Monday, April 12, 2010 - 11:00am - 11:45am
Alexei Novikov (The Pennsylvania State University)
Consider a Brownian particle in a deterministic time-independent incompressible flow in a bounded domain. We are interested how flow affects the expected exit time, the time the particle needs to reach the boundary of the domain. In particular, whether the presence of the flow decreases the maximum of this expected exit time. One would expect that any stirring improves mixing, thus decreasing the expected exit time. We will show that generally it is not true in two dimensions. This is a joint work with G.Iyer, L.Ryzhik, and A.Zlatos.
Wednesday, April 14, 2010 - 11:00am - 11:45am
Jean-Luc Thiffeault (University of Wisconsin, Madison)
Keywords: stirring, mixing, biomixing, Brownian motion.

Abstract: As fish or other bodies move through a fluid, they stir their
surroundings. This can be beneficial to some fish, since the plankton
they eat depends on a well-stirred medium to feed on nutrients.
Bacterial colonies also stir their environment, and this is even more
crucial for them since at small scales there is no turbulence to help
mixing. It has even been suggested that the total biomass in the
Tuesday, December 8, 2009 - 10:50am - 11:30am
Eric Shaqfeh (Stanford University)
Keywords: Brownian rods, surfboards, drug delivery, capsules, vesicles, margination
Friday, October 16, 2009 - 9:15am - 9:55am
Hector Ceniceros (University of California)
Keywords: Field theoretic polymer models, flow-structure interaction, mesoscale models, phase field models.

Abstract: We will present examples of field theoretic models of multi-component and complex fluids and discuss their main computational challenges and recent advances. We will start with simple phase field based models and progress to a class of field-theoretic models that incorporate exact thermodynamics. In particular, we will
Thursday, October 15, 2009 - 9:00am - 9:40am
John Brady (California Institute of Technology)
Keywords: Colloidal dispersions, Brownian motion, rheology

Abstract: The motion of a single individual particle in a complex
material is fundamental to understanding the dynamical
properties of the material. Monitoring such motion has given
rise to a suite of experimental techniques collectively known
as ‘microrheology,’ with the ability to probe the viscoelastic
properties of soft heterogeneous materials (e.g. polymer
solutions, colloidal dispersions, biomaterials, etc.) at the
Wednesday, October 14, 2009 - 9:45am - 10:25am
Tony Ladd (University of Florida)
I will outline the application of the fluctuating lattice-Boltzmann equation
to the simulation of polymer solutions. Then I will describe a numerical
assessment of the accuracy of lattice-Boltzmann methods for polymers, by
comparison with Brownian dynamics simulations on a similar model system.
We will examine the relaxation spectrum of an isolated chain and the
migration of individual chains in shear and pressure-driven flows.


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