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Noise to signal transition: work obtained from noise studied by the optical tweezers
Šiler, Martin ; Filip, R. ; Jákl, Petr ; Brzobohatý, Oto ; Zemánek, Pavel
The noise-to-signal transitions are very interesting processes in physics as they might transform environmental noise to useful mechanical effects. In this contribution we introduce the problem of stochastic noise-to-signal transition of overdamped Brownian motion of a particle in the cubic potential. The particle reaches thermal equilibrium with its environment in the quadratic potential which is suddenly swapped to the cubic potential. We predict simultaneous increase of both the displacement and signal-to-noise ratio in the cubic potential for the position linearly powered by temperature of the particle environment. Further, we propose a feasible experimental setup for proof-of-the-principle experiment that uses methods of optical trapping in shaped laser beams providing cubic and quadratic potentials.
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Stochastic equations and numerical solution of pricing option model
Janečka, Adam ; Jablonský, Josef (advisor) ; Pelikán, Jan (referee)
In the present work, we study the topic of stochastic differential equations, their numerical solution and solution of models for pricing of options which follow from stochastic differential equations using the Itô calculus. We present several numerical methods for solving stochastic differential equations. These methods are then implemented in MATLAB and we investigate their properties, especially their convergence characteristics. Furthermore, we formulate two models for pricing of European call options. We solve these models using a variant of the spectral collocation method, again in MATLAB.
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Stochastické rovnice a stochastické metody v parciálních diferenciálních rovnicích
Maslowski, Bohdan
In the first part of the paper, basic notions of stochastic analysis and probability theory are recalled, including the concept of stochastic integration, and some basic results of the theory of partial differential equations are reviewed. The second part of the paper is a review of applications of stochastic analysis techniques in deterministic PDE theory. The last part contains a brief introduction to stochastic PDEs and other stochastic infinite dimensional systems.
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