A Serendipitous Journey through Stochastic Processes

• In this PhD thesis we will present some new insights in different problems in the field of stochastic processes. A stochastic resonance system is studied using path integral techniques, originally developed in quantum field theory, to recover the optimal means through which noise self-organises before a rare transition from one potential well to the other. These results allow one to determine precursors to a rare events in such system.We then study the survival probability of an autonomous Ornstein-Uhlenbeck process using the asymptotic matching techniques developed in fluid dynamics. Here, we obtain a simple analytical expression for this quantity that exhibits a good agreement with numerical determination.Next, rare events in similar systems are studied using a recurrent neural network to model the noisy part of the signal. The neural network facilitates the prediction of future noise realisations and hence rare transitions.Using a combination of analytical and numerical techniques a low-dimensional model is constructed and it is able to predict and to reproduce the main dynamical and equilibrium features of the El Ni\~no and Southern Oscillation (ENSO), the largest inter-annual variability phenomenon in the tropical Pacific which has a global impact on climate.Using the results obtained for the survival probability of the Ornstein-Uhlenbeck process, an approximate analytical solution for the probability density function and the response is derived for a stochastic resonance system in the non-adiabatic limit.Finally, the Landauer principle is applied to investigate the thermodynamics of finite time information erasure, using a model of a Brownian particle in a symmetric double-well potential. Analytical tools are derived to calculate the distribution of the work required to erase information through an arbitrary continuous erasure protocol, and the theoretical findings are numerically validated.

Ämnesord

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

Nyckelord

Stochastic process

statistical physics

machine learning

Theoretical Physics

teoretisk fysik

Publikations- och innehållstyp

vet (ämneskategori)

dok (ämneskategori)