Maxwell Institute Probability Day

13th May 2016

• The Maxwell Institute Probability Day is an annual event organised jointly between the probability and stochastic analysis groups at University of Edinburgh and Heriot-Watt University. The event aims at fostering interactions between these research groups and neighbouring universities in the UK.
  
  
• Organisers.
  
  
  • Sergey Foss (Heriot Watt)
  • Istvan Gyongy (University of Edinburgh)
  • Michela Ottobre (Heriot Watt)
  • David Siska (University of Edinburgh)



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• Venue. Lecture Theatre 183, Old College, 68 South Bridge, Edinburgh EH8 9YL



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• Registration. The event is open to all. For catering purposes, please fill out this doodle poll by the 5th of May if you would like to attend. We strongly encourage participation of PhD students, Postdocs and young researchers.



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• Programme.
  
  
  • 12.00-12.45       Lunch
  • 12.45 - 13.30     Tusheng Zhang (Manchester)   Lattice Approximations of Reflected Stochastic Partial Differential Equations Driven by Space-Time White Noise
  • 13.30 - 14.15     Dominic Breit (Heriot Watt)   Numerical approximation of stochastic p-Laplace type system
  • 14.15 - 14.40     Timofei Prasolov (Heriot Watt)   Tail asymptotics of meeting times of dependent agents
  • 14.40 - 15.10     Coffe Break
  • 15.10 - 15.55     Tolga Tezcan (London Business School)   Yardstick Competition for Service Systems
  • 15.55 - 16.40     Ruth King (University of Edinburgh)   Fitting state-space models to data using an approximate hidden Markov model



• Abstracts
  
  
  • Tusheng Zhang (Manchester)   Lattice Approximations of Reflected Stochastic Partial Differential Equations Driven by Space-Time White Noise
    We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space-time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the scheme, we study the existence and uniqueness of solutions of Skorohod-type deterministic systems on time-dependent domains. We also need to establish the convergence of an approximation scheme for deterministic parabolic obstacle problems.
  
  
  • Dominic Breit (Heriot Watt)   Numerical approximation of stochastic p-Laplace type system.
    We consider systems of stochastic evolutionary equations of the p-Laplace type. We study finite element space-time discretization and prove convergence together with rates. The approximation error is measured with the quasi norm.
  
  
  • Timofei Prasolov (Heriot Watt)   Tail asymptotics of meeting times of dependent agents
    Motivated by work of N. Litvak and P. Robert "A scaling analysis of a Cat and Mouse Markov chain", we started to analyse more general object, working name for which is "Dog, Cat and Mouse Markov chain". Here coordinate of "Dog" is a simple random walk in integer space. Movement of "Cat" depends on "Dog" and movement of "Mouse" depends on "Cat". We analyse the position of this system after a long run by finding tail asymptotics of meeting times of all three agents.
  
  
  • Tolga Tezcan (London Business School)   Yardstick Competition for Service Systems
    Yardstick competition is a regulatory scheme for local monopolists (e.g., hospitals), where the monopolists’ reimbursement is linked to its performance relative to other equivalent monopolists. This regulatory scheme is known to work well in providing cost-reduction incentives and offers the theoretical underpinning behind the hospital prospective reimbursement system used throughout the developed world. This paper investigates how yardstick competition performs in service systems (e.g., hospital emergency departments), where in addition to incentivizing cost reduction, the regulator's goal is to provide incentives to reduce customer waiting times. We show that i) the form of yardstick competition used in practice results in inefficiently long waiting times; ii) yardstick competition can be appropriately modified to achieve the dual goal of cost and waiting-time reduction, and present several extensions that help guide on how it could be used in practice.
  
  
  • Ruth King (University of Edinburgh)   Fitting state-space models to data using an approximate hidden Markov model
    Many mathematical models can be expressed in the form of a state-space model. For such models the model can be separated into two parts: (i) system process - describing the evolution of the true underlying process over time (assumed to be continuous); and (ii) observation process - describing what we observe given the true state of the process. Typically we wish to obtain inference on the underlying system process, estimating the associated model parameters to further our understanding of the system. However, the corresponding likelihood of the observed data is typically analytically intractable. Estimates of the parameters can be obtained using the Kalman filter assuming a linear Gaussian model. We discuss an alternative approach that can be generally applied to non-linear and non-Gaussian state-space models using an approximate (discretised) hidden Markov model likelihood framework.
    
    

The organizers gratefully acknowledge financial support from the Maxwell Institute