Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 28 for “"Fractional Brownian Motion"”.
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Fractional Brownian motion and dynamic approach to complexity.
The dynamic approach to fractional Brownian motion (FBM) establishes a link between non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a non-vanishing memory of their past time evolution. It is …
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Maximum likelihood estimation of fractional Brownian motion and Markov noise parameters
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1992.
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STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION AND THEIR GENERALIZATIONS
… equation with infinite memory driven by a fractional Brownian motion with Hurst parameter $H>1/2$. We prove an existence and uniqueness result of the solution to the stochastic differential equation. We investigate the dependence of the solution on the initial condition and the existence of …
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Inferring influence in dynamic networks and multiple sampling for estimation of fractional Brownian motion
Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-05-01
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Monte Carlo Methods for Derivative Pricing of Stochastic Volatility Models Driven by Fractional Brownian Motion
… prices with stochastic volatilities driven by fractional Brownian motion. Price paths and their endpoints are used to obtain a Monte Carlo value estimate of vanilla european options, lookback options as well as variance swaps. Underlying models for price movements are driven by stochastic …
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Asymptotics of the Rough Heston Model
… recent explosion of work on rough volatility and fractional Brownian motion has led to the development of a new generation of stochastic volatility models. Such models are able to capture a wide range of stylised facts that classical models simply do not. While these models have sound mathematical …
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Signal detection in fractional Gaussian noise and an RKHS approach to robust detection and estimation
… first part, the problem of signal detection in fractional Gaussian noise is considered. To facilitate the study of this problem, several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented. In particular, this reproducing kernel Hilbert space is …
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On Self-Similar Gaussian Processes
… part we have shown a decomposition of the bifractional Brownian motion with parameters H,K into the sum of a fractional Brownian motion with Hurst parameter HK plus a stochastic process with absolutely continuous trajectories. Some applications of this decomposition are discussed. In the …
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An Exponential Formula for Random Variables Generated by Multiple Brownian Motions
… for random variables generated by classical Brownian motion, Lévy processes and fractional Brownian with Hurst index greater than 1/2.The relationship between the conditional expectation of a random variable (or fractional conditional expectation in the case of fractional Brownian motion)and …
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FRACTAL BASED FRAMEWORK FOR TIME SERIES VOLATILITY PREDICTION
… modelling asset behaviour by bringing together fractional Brownian motion (fBm), fuzzy logic, and jump processes, all aligned with the no–arbitrage principle. In particular, our mathematical developments include fBm defined through Mandelbrot–Van Ness kernels, and advanced mathematical tools …
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Some application of Malliavin calculus to SPDE and convergence of densities
… Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter H<1/2. To establish such a formula, we introduce and study a nonlinear stochastic integral of the Gaussian noise. The existence of the Feynman-Kac integral then follows from the exponential …
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A review of current Rough Volatility Methods
… The models of rough dynamics are built upon the fractional Brownian Motion and its associated powerlaw kernel. One such model is called the Rough Heston, an extension of the Classical Heston model, and is the main model of focus for this dissertation. To implement the Rough Heston, fractional …
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Long-memory stochastic volatility model calibration using deep neural nets
… of stochastic volatility models characterized by fractional Brownian motion. The specific challenge with these long-memory models is that they are non-Markovian in nature and simulation can be time-consuming and costly. We show that by using neural networks we can capture these non-Markovian …
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Time keeping in myriad networks : theories, solutions and applications
… cross traffic exhibiting long-range dependence (fractional Brownian motion cross-traffic) or no dependence at all (white Gaussian case). We conclude with applications over packet switched networks that require time synchronization, like spatial filtering (beam-forming). The suite of algorithms …
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Bayesian estimation of self-similarity exponent
… considers the realizations of the processes of fractional Brownian motion and fractional Gaussian noise. Additionally, applications to real-world data, such as the data of water level of the Nile River and fixational eye movements are also discussed.
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Free products of operator spaces and free Markov processes
… non-commutative notion generalizes that of free Brownian motion and free Levy processes. Some free Markov processes are realized as solutions to free stochastic differential equations driven by free Levy processes. A special and rather interesting kind of free Markov processes, free …
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Complex dynamics of a microwave time-delayed feedback loop
… behaviors can have properties of a regular or fractional Brownian motion. By unidirectional coupling two systems in the baseband, envelope synchronization between two deterministic Brownian motions can be achieved.
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Sparse selection in Cox models with functional predictors
… large sample properties of the estimators, the fractional Brownian motion assumption is posed for the trajectories for mathematical tractability. Simulations are conducted to evaluate the finite sample performance of the methods, and a way to construct the confidence interval for the location …
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Phononic metamaterials based on complex geometries : "a new kind of metamaterial"
… analytical model. For metamaterials based on fractional Brownian motion, the Hurst constant is found to be a good indicator of phononic behavior of the system, besides other parameters studied. Our findings does not only expand the repertoire for novel materials by introducing the ubiquitous …
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