143 research outputs found
Large Deviations for processes on half-line
We consider a sequence of processes defined on half-line for all non negative
t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in
the space of continuous functions with a new metric that is more sensitive to
behaviour at infinity than the uniform metric. LDP is established for Random
Walks, Diffusions, and CEV model of ruin, all defined on the half-line. LDP in
this space is "more precise" than that with the usual metric of uniform
convergence on compacts.Comment: 23 page
On the emergence of random initial conditions in fluid limits
The paper presents a phenomenon occurring in population processes that start
near zero and have large carrying capacity. By the classical result of
Kurtz~(1970), such processes, normalized by the carrying capacity, converge on
finite intervals to the solutions of ordinary differential equations, also
known as the fluid limit. When the initial population is small relative to
carrying capacity, this limit is trivial. Here we show that, viewed at suitably
chosen times increasing to infinity, the process converges to the fluid limit,
governed by the same dynamics, but with a random initial condition. This random
initial condition is related to the martingale limit of an associated linear
birth and death process
Escape from the boundary in Markov population processes
Density dependent Markov population processes in large populations of size
were shown by Kurtz (1970, 1971) to be well approximated over finite time
intervals by the solution of the differential equations that describe their
average drift, and to exhibit stochastic fluctuations about this deterministic
solution on the scale that can be approximated by a diffusion
process. Here, motivated by an example from evolutionary biology, we are
concerned with describing how such a process leaves an absorbing boundary.
Initially, one or more of the populations is of size much smaller than , and
the length of time taken until all populations have sizes comparable to
then becomes infinite as . Under suitable assumptions, we show
that in the early stages of development, up to the time when all populations
have sizes at least , for , the process can be
accurately approximated in total variation by a Markov branching process.
Thereafter, the process is well approximated by the deterministic solution
starting from the original initial point, but with a random time delay.
Analogous behaviour is also established for a Markov process approaching an
equilibrium on a boundary, where one or more of the populations become extinct.Comment: 50 page
Dynamic PID loop control
The Horizontal Test Stand (HTS) SRF Cavity and Cryomodule 1 (CM1) of eight
9-cell, 1.3GHz SRF cavities are operating at Fermilab. For the cryogenic
control system, how to hold liquid level constant in the cryostat by regulation
of its Joule-Thompson JT-valve is very important after cryostat cool down to
2.0 K. The 72-cell cryostat liquid level response generally takes a long time
delay after regulating its JT-valve; therefore, typical PID control loop should
result in some cryostat parameter oscillations. This paper presents a type of
PID parameter self-optimal and Time-Delay control method used to reduce
cryogenic system parameters' oscillation.Comment: 7 pp. Cryogenic Engineering Conference and International Cryogenic
Materials Conference CEC-ICMC 2011, 13-17 June 2011. Spokane, Washingto
Plate Fin Heat Exchanger Model with Axial Conduction and Variable Properties
Future superconducting radio frequency (SRF) cavities, as part of Project X
at Fermilab, will be cooled to superfluid helium temperatures by a cryogenic
distribution system supplying cold supercritical helium. To reduce vapor
fraction during the final Joule-Thomson (J-T) expansion into the superfluid
helium cooling bath, counter-flow, plate-fin heat exchangers will be utilized.
Due to their compact size and ease of fabrication, plate-fin heat exchangers
are an effective option. However, the design of compact and high-effectiveness
cryogenic heat exchangers operating at liquid helium temperatures requires
consideration of axial heat conduction along the direction of flow, in addition
to variable fluid properties. Here we present a numerical model that includes
the effects of axial conduction and variable properties for a plate fin heat
exchanger. The model is used to guide design decisions on heat exchanger
material choice and geometry. In addition, the J-T expansion process is modeled
with the heat exchanger to analyze the effect of heat load and cryogenic supply
parameters.Comment: 8 pp. Cryogenic Engineering Conference and International Cryogenic
Materials Conference CEC-ICMC, 13-17 June 2011, Spokane, Washingto
Capital allocation for credit portfolios with kernel estimators
Determining contributions by sub-portfolios or single exposures to
portfolio-wide economic capital for credit risk is an important risk
measurement task. Often economic capital is measured as Value-at-Risk (VaR) of
the portfolio loss distribution. For many of the credit portfolio risk models
used in practice, the VaR contributions then have to be estimated from Monte
Carlo samples. In the context of a partly continuous loss distribution (i.e.
continuous except for a positive point mass on zero), we investigate how to
combine kernel estimation methods with importance sampling to achieve more
efficient (i.e. less volatile) estimation of VaR contributions.Comment: 22 pages, 12 tables, 1 figure, some amendment
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