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Relevant bibliographies by topics / Volterrovské procesy

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Dissertations / Theses

Academic literature on the topic 'Volterrovské procesy'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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Dissertations / Theses on the topic "Volterrovské procesy"

1

Kratochvíl, Matěj. "Frakcionální Brownův pohyb ve financích." Master's thesis, 2016. http://www.nusl.cz/ntk/nusl-352586.

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This thesis deals with the stochastic integral with respect to Gaussian processes, which can be expressed in the form Bt = t 0 K(t, s)dWs. Here W stands for a Brownian motion and K for a square integrable Volterra kernel. Such processes generalize fractional Brownian motion. Since these processes are not semimartin- gales, Itô calculus cannot be used and other methods must be employed to define the stochastic integral with respect to these proceses. Two ways are considered in this thesis. If both the integrand and the process B are regular enough, it is possible to define the integral in the p

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2

Kršek, Daniel. "Semilineární stochastické evoluční rovnice." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448080.

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Stochastic partial differential equations have proven useful in many applied areas of mathematics, such as physics or mathematical finance. A major part of such equations consists of linear equations with additive noise. In certain cases, however, the drift part of the differential equation additionally contains a possibly problematic non-linear term, which makes it unsolvable by the standard methods and even a solution in the mild sense may be out of reach. In such situations, we may still find a solution in the weak sense by employing a suitable transformation of the probability space. This

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3

Pacák, Daniel. "Odhad parametru ve stochastických diferenciálních rovnicích." Master's thesis, 2020. http://www.nusl.cz/ntk/nusl-434533.

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In the Thesis the problem of estimating an unknown parameter in a stochastic dif- ferential equation is studied. Linear equations with Volterra process as the source of noise are considered. Firstly, the properties of Volterra processes and the properties of stochastic integral with respect to a Volterra process are presented. Secondly, the prop- erties of the solution to the equation under consideration are discussed. This includes the existence of the strictly stationary solution, the properties of such solution and ergodic results. These results are then generalized to equations with a mixe

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4

Čoupek, Petr. "Stochastické evoluční rovnice." Doctoral thesis, 2017. http://www.nusl.cz/ntk/nusl-368518.

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Stochastic Evolution Equations Petr Čoupek Doctoral Thesis Abstract Linear stochastic evolution equations with additive regular Volterra noise are studied in the thesis. Regular Volterra processes need not be Gaussian, Markov or semimartingales, but they admit a certain covariance structure instead. Particular examples cover the fractional Brownian motion of H > 1/2 and, in the non-Gaussian case, the Rosenblatt process. The solution is considered in the mild form, which is given by the variation of constants formula, and takes values either in a separable Hilbert space or the space Lp(D, µ) fo

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5

Čoupek, Petr. "Stochastické integrály řízené isonormálními gaussovskými procesy a aplikace." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-328307.

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Stochastic Integrals Driven by Isonormal Gaussian Processes and Applications Master Thesis - Petr Čoupek Abstract In this thesis, we introduce a stochastic integral of deterministic Hilbert space valued functions driven by a Gaussian process of the Volterra form βt = t 0 K(t, s)dWs, where W is a Brownian motion and K is a square integrable kernel. Such processes generalize the fractional Brownian motion BH of Hurst parameter H ∈ (0, 1). Two sets of conditions on the kernel K are introduced, the singular case and the regular case, and, in particular, the regular case is studied. The main result

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