We present a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. The PDF is represented as a path integral and is evaluated using the saddle-point method. It factorizes into ...
In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the ...
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover th ...
Advances in data acquisition technologies and supercomputing for large-scale simulations have led to an exponential growth in the volume of spatial data. This growth is accompanied by an increase in data complexity, such as spatial density, but also by mor ...
In this thesis, I aim to contribute to the research towards improving the sustainability of habitat life in streams affected by anthropogenic activities. With the growing trend of altering natural water regimes due to hydropower operations, irrigation, and ...
We develop new analytic methods to accurately describe the formation of cosmic large-scale structure. These methods are based on the path integral formalism and allows one to efficiently address a number of long-standing problems in the field.
We describe ...
Improved water management strategies necessitate a solid understanding of environmental impacts associated with various flow release policies. Habitat suitability models use hydrodynamic simulations to generate weighted usable area curves, which are useful ...
The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, ...
