# "micro-conference" on Probability Theory & Its Applications

*by Andrew Barbour, Daniel Dufresne, Fima Klebaner, Owen Jones*

*Institution:*

*Date: Tue 27th March 2012*

*Time: 4:15 PM*

*Location: Old Geology Theatre 1, Parkville Campus, Melbourne Uni*

*Abstract*: Dear All,

We are delighted to announce that a "micro-conference" on Probability Theory & Its Applications proudly supported by MASCOS will be held at the University of Melbourne on Tuesday, 27 March 2012 afternoon (16:15-19:05).

There will be four 30+5' talks, to be followed by a dinner. This is already the fourth event of this kind, and we plan to continue running such events on a more or less regular basis, alternating locations (UofM & Monash), as we did it last year.

Apologies for possible multiple posting, but please feel free to forward the message to anybody who may be interested (if you are not based at the Dept of Moths & Stats, Uni Melbourne, most of your "local" colleagues won’t be receiving this email!).

Before providing more info on the event, let me say this (as it's important!):

++ If you are going to come to the talks, please email me -- we will need that information for tea/coffee catering purposes.

++ Plus, please let me know if you will be joining us for dinner (planned to start around 7:20pm, at a local restaurant -- most likely, an Italian place @ Lygon Street, Carlton), as we need the headcount for booking. You partner would be more than welcome as well. (Just to be on the safe side: at the dinner, we will have to pay for ourselves.)

RSVP by Monday, 19 March 2012. Thanks!

More detail on the event itself (the abstracts of the talks are at the end of the message):

++++++++++++++++++++ PROGRAM +++++++++++++++++++++

Tuesday, 27 March 2012, 4:20pm +

Venue: Old Geology Theatre 1, Parkville Campus, Melbourne Uni

** 4:20-4:50pm [4:55 end of question time]

Talk 1: The asymptotics of the Aldous gossip process.

Speaker: Andrew Barbour (Melbourne & Monash Unis)

** 4:55-5:25pm [5:30 end of question time]

Talk 2: Gram-Charlier Distributions

Speaker: Daniel Dufresne (Melbourne Uni)

** 5:30-6:00pm

Tea/coffee break (tearoom, Richard Berry Bldg)

** 6:00-6:30pm [6:35 end of question time]

Talk 3: Law of Large Numbers for the age distribution in population

dependent branching processes

Speaker: Fima Klebaner (Monash Uni)

** 6:35-7:05pm [7:10 end of question time]

Talk 4: Exact simulation of diffusions

Speaker: Owen Jones (Melbourne Uni)

** 7:15pm +

Dinner (venue TBA)

+++++++++++++++ END OF PROGRAM ++++++++++++++++++++

Looking forward to seeing you at the micro-conference, and don't forget to let me know that you are coming (if you are coming)!

Cheers,

kostya borovkov

+++++++++++++++ APPENDIX: Abstracts of the talks +++++++++++++++++

Talk 1: The asymptotics of the Aldous gossip process.

Speaker: Andrew Barbour (Universität Zürich & Melbourne Uni)

Abstract: As a model for the spread of gossip, Aldous used the (discrete) 2-D torus to represent space, with gossip spreading between neighbours, but also occasionally at long range. The development of a continuous space version was shown by Durrett and Chatterjee to have some randomness at the start, but thereafter to run an almost deterministic course, described by a mysterious function $h$, that also appears in Aldous's paper. Here, we explain the asymptotics, and identify $h$, entirely in terms of branching processes. Our arguments remain valid for the spread on quite general, locally homogeneous manifolds, in any number of dimensions.

Talk 2: Gram-Charlier Distributions

Speaker: Daniel Dufresne (Melbourne Uni)

Abstract: Not the greatest model for stock returns, Gram-Charlier distributions still have some interest. Will talk about their history and properties, maybe option pricing.

Talk 3: Law of Large Numbers for the age distribution in population

dependent branching processes

Speaker: Fima Klebaner (Monash Uni)

Abstract. We consider a population of particles evolving in continuous time. If the lifespans are not exponential such process (the Belman-Harris process) is not Markov. However, considered as a collection of ages, as a finite counting measure $A=\sum_a \delta_a,$ it is Markov. We give the generator of such process, and its

semimartingale decomposition. Assuming further that the parameters (lifespans, offspring distributions) depend on the population composition, in such a way that it is supercritical below some threshold K and subcritical above it. We prove Law of Large Numbers for the measure valued process $\frac{1}{K}A_t^K$ as $K\to\infty$, and describe the measure-valued limit $A_t$. Convergence is shown in the space of trajectories, the Skorohod space $D(R^+,M(R^+))$, where $M(R^+))$ is the space of measures on $R^+$ metrizable by weak convergence. This is joint work with K. Hamza (Monash) and P. Jagers (Chalmers).

Talk 4: Exact simulation of diffusions

Speaker: Owen Jones (Melbourne Uni)

Abstract: Some recent results by Nan Chen (Hong Kong) and Giesecke and Smelovy (Stanford), on the exact simulation of diffusion, are described. Unlike the approach of Beskos and Roberts (2005), the diffusion is simulated on a regular spatial lattice, rather than at regular points in time.