Dissertations / Theses on the topic 'Stochastic process'
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PEREIRA, RICARDO VELA DE BRITTO. "VOLATILITY: A HIDDEN STOCHASTIC PROCESS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2010. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=16816@1.
Full textA volatilidade é um parâmetro importante de modelagem do mercado financeiro. Ela controla a medida de risco associado à dinâmica estocástica de preço do título financeiro, afetando também o preço racional dos derivativos.Existe evidência empírica que a volatilidade é por sua vez também um processo estocástico, subjacente ao dos preços. Assim, a volatilidade não pode ser observada diretamente e tem que ser estimada, constituindo-se de um processo estocástico escondido.Nesta dissertação, consideramos um estimador para a volatilidade diária do índice da BOVESPA, baseado em banco de dados intradiários. Fazemos uma análise estatística descritiva da série temporal obtida, obtendo-se a função densidade de probabilidade, os momentos e as correlações. Comparamos os resultados empíricos com as previsões teóricas de vários modelos de volatilidade estocástica. Consideramos a classe de equações de Itô-Langevin formada por um processo de reversão à média e um processo difusivo de Wiener generalizado, com componentes de ruído multiplicativo e/ou aditivo. A partir dessa análise, é sugerido um modelo para descrever as flutuações de volatilidade dos preços do mercado acionário brasileiro.
Volatility is a key model parameter of the financial market. It controls the risk associated to the stochastic dynamics of the asset prices and also affects the rational price of derivative products. There are empirical evidences that the volatility is also a stochastic process, underlined to the price one. Therefore, the volatility is not directly observed and must be estimated, constituting a hidden stochastic process. In this work, we consider an estimate for the daily volatility of the BOVESPA index, computed from the intraday database. We perform a descriptive statistical analysis of the resulting time series, obtaining the probability density function, moments and correlations. We compare the empirical outcomes with the theoretical forecasts of many stochastic volatility models. We consider the class of Itô-Langevin equations composed by a mean reverting process and a generalized diffusive Wiener process with multiplicative and/or additive noise components. From this analysis, we propose a model that describes the volatility fluctuations of the Brazilian stock market.
Catalão, André Borges [UNESP]. "Modelagem estocástica de opções de câmbio no Brasil: aplicação de transformada rápida de Fourier e expansão assintótica ao modelo de Heston." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/88592.
Full textNeste trabalho estudamos a calibração de opções de câmbio no mercado brasileiro utilizando o processo estocástico proposto por Heston [Heston, 1993], como uma alternativa ao modelo de apreçamento de Black e Scholes [Black e Scholes,1973], onde as volatilidades implícitas de opções para diferentes preços de exercícios e prazos são incorporadas ad hoc. Comparamos dois métodos de apreçamento: o método de Carr e Madan [Carr e Madan, 1999], que emprega transfomada rápida de Fourier e função característica, e expansão assintótica para baixos valores de volatilidade da variância. Com a nalidade de analisar o domínio de aplicabilidade deste método, selecionamos períodos de alta volatilidade no mercado, correspondente à crise subprime de 2008, e baixa volatilidade, correspondente ao período subsequente. Adicionalmente, estudamos a incorporação de swaps de variância para melhorar a calibração do modelo
In this work we study the calibration of forex call options in the Brazilian market using the stochastic process proposed by Heston [Heston, 1993], as an alternative to the Black and Scholes [Black e Scholes,1973] pricing model, in which the implied option volatilities related to di erent strikes and maturities are incorporated in an ad hoc manner. We compare two pricing methods: one from Carr and Madan [Carr e Madan, 1999], which uses fast Fourier transform and characteristic function, and asymptotic expantion for low values of the volatility of variance. To analyze the applicability of this method, we select periods of high volatility in the market, related to the subprime crisis of 2008, and of low volatility, correspondent to the following period. In addition, we study the use of variance swaps to improve the calibration of the model
Pihnastyi, O. M., and V. D. Khodusov. "Stochastic equation of the technological process." Thesis, Igor Sikorsky Kyiv Polytechnic Institute, 2018. http://repository.kpi.kharkov.ua/handle/KhPI-Press/39059.
Full textGibellato, Marilisa Gail. "Stochastic modeling of the sleep process." The Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=osu1110318321.
Full textGibellato, M. G. "Stochastic modeling of the sleep process." Connect to this title online, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1110318321.
Full textTitle from first page of PDF file. Document formatted into pages; contains xvii, 188 p.; also includes graphics Includes bibliographical references (p. 184-188). Available online via OhioLINK's ETD Center
Bohnenkamp, Henrik. "Compositional solution of stochastic process algebra models." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=965593193.
Full textRogge-Solti, Andreas, Ronny S. Mans, der Aalst Wil M. P. van, and Mathias Weske. "Repairing event logs using stochastic process models." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6679/.
Full textUnternehmen optimieren ihre Geschäftsprozesse laufend um im kompetitiven Umfeld zu bestehen. Das Ziel von Process Mining ist es, bedeutende Erkenntnisse aus prozessrelevanten Daten zu extrahieren. In den letzten Jahren sorgte Process Mining bei Experten, Werkzeugherstellern und Forschern zunehmend für Aufsehen. Traditionell wird dabei angenommen, dass Ereignisprotokolle die tatsächliche Ist-Situation widerspiegeln. Dies ist jedoch nicht unbedingt der Fall, wenn prozessrelevante Ereignisse manuell erfasst werden. Ein Beispiel hierfür findet sich im Krankenhaus, in dem das Personal Behandlungen meist manuell dokumentiert. Vergessene oder fehlerhafte Einträge in Ereignisprotokollen sind in solchen Fällen nicht auszuschließen. In diesem technischen Bericht wird eine Methode vorgestellt, die das Wissen aus Prozessmodellen und historischen Daten nutzt um fehlende Einträge in Ereignisprotokollen zu reparieren. Somit wird die Analyse unvollständiger Ereignisprotokolle erleichtert. Die Reparatur erfolgt mit einer Kombination aus stochastischen Petri Netzen, Alignments und Bayes'schen Netzen. Die Ergebnisse werden mit synthetischen Daten und echten Daten eines holländischen Krankenhauses evaluiert.
Kabouris, John C. "Stochastic control of the activated sludge process." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/20306.
Full textTribastone, Mirco. "Scalable analysis of stochastic process algebra models." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4629.
Full textPathmanathan, S. "The poisson process in quantum stochastic calculus." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249564.
Full textBradley, Jeremy Thomas. "Towards reliable modelling with stochastic process algebras." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302166.
Full textBalijepalli, Narasimha Chandrasekhar. "Stochastic process models for dynamic traffic assignment." Thesis, University of Leeds, 2007. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.436385.
Full textNi, Hao. "The expected signature of a stochastic process." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:e0b9e045-4c09-4cb7-ace9-46c4984f16f6.
Full textOhara, Noriaki. "Numerical and stochastic upscaling of snowmelt process /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2003. http://uclibs.org/PID/11984.
Full textBeal, Joshua M. "Matching Problems for Stochastic Processes." Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1367500889.
Full textSaha, Chiranjib. "Advances in Stochastic Geometry for Cellular Networks." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99835.
Full textDoctor of Philosophy
The high speed global cellular communication network is one of the most important technologies, and it continues to evolve rapidly with every new generation. This evolution greatly depends on observing performance-trends of the emerging technologies on the network models through extensive system-level simulations. Since these simulation models are extremely time-consuming and error prone, the complementary analytical models of cellular networks have been an area of active research for a long time. These analytical models are intended to provide crisp insights on the network behavior such as the dependence of network performance metrics (such as coverage or rate) on key system-level parameters (such as transmission powers, base station (BS) density) which serve as the prior knowledge for more fine-tuned simulations. Over the last decade, the analytical modeling of the cellular networks has been driven by stochastic geometry. The main purpose of stochastic geometry is to endow the locations of the base stations (BSs) and users with probability distributions and then leverage the properties of these distributions to average out the spatial randomness. This process of spatial averaging allows us to derive the analytical expressions of the system-level performance metrics despite the presence of a large number of random variables (such as BS and user locations, channel gains) under some reasonable assumptions. The simplest stochastic geometry based model of cellular networks, which is also the most tractable, is the so-called Poisson point process (PPP) based network model. In this model, users and BSs are assumed to be distributed as independent homogeneous PPPs. This is equivalent to saying that the users and BSs independently and uniformly at random over a plane. The PPP-based model turned out to be a reasonably accurate representation of the yesteryear’s cellular networks which consisted of a single tier of macro BSs (MBSs) intended to provide a uniform coverage blanket over the region. However, as the data-hungry devices like smart-phones, tablets, and application like online gaming continue to flood the consumer market, the network configuration is rapidly deviating from this baseline setup with different spatial interactions between BSs and users (also termed spatial coupling) becoming dominant. For instance, the user locations are far from being homogeneous as they are concentrated in specific areas like residential and commercial zones (also known as hotspots). Further, the network, previously consisting of a single tier of macro BSs (MBSs), is becoming increasingly heterogeneous with the deployment of small cell BSs (SBSs) with small coverage footprints and targeted to serve the user hotspots. It is not difficult to see that the network topology with these spatial couplings is quite far from complete spatial randomness which is the basis of the PPP-based models. The key contribution of this dissertation is to enrich the stochastic geometry-based mathematical models so that they can capture the fine-grained spatial couplings between the BSs and users. More specifically, this dissertation contributes in the following three research directions. Direction-I: Modeling Spatial Clustering. We model the locations of users and SBSs forming hotspots as Poisson cluster processes (PCPs). A PCP is a collection of offspring points which are located around the parent points which belong to a PPP. The coupling between the locations of users and SBSs (due to their user-centric deployment) can be introduced by assuming that the user and SBS PCPs share the same parent PPP. The key contribution in this direction is the construction of a general HetNet model with a mixture of PPP and PCP-distributed BSs and user distributions. Note that the baseline PPP-based HetNet model appears as one of the many configurations supported by this general model. For this general model, we derive the analytical expressions of the performance metrics like coverage probability, BS load, and rate as functions of the coupling parameters (e.g. BS and user cluster size). Direction-II: Modeling Coupling in Wireless Backhaul Networks. While the deployment of SBSs clearly enhances the network performance in terms of coverage, one might wonder: how long network densification with tens of thousands of SBSs can meet the everincreasing data demand? It turns out that in the current network setting, where the backhaul links (i.e. the links between the BSs and core network) are still wired, it is not feasible to densify the network beyond some limit. This backhaul bottleneck can be overcome if the backhaul links also become wireless and the backhaul and access links (link between user and BS) are jointly managed by an integrated access and backhaul (IAB) network. In this direction, we develop the analytical models of IAB-enabled HetNets where the key challenge is to tackle new types of couplings which exist between the rates on the wireless access and backhaul links. Such couplings exist due to the spatial correlation of the signal qualities of the two links and the number of users served by different BSs. Two fundamental insights obtained from this work are as follows: (1) the IAB HetNets can support a maximum number of users beyond which the network performance drops below that of a single-tier macro-only network, and (2) there exists a saturation point of SBS density beyond which no performance gain is observed with the addition of more SBSs. Direction-III: Modeling Repulsion. In this direction, we focus on modeling another aspect of spatial coupling imposed by the intra-point repulsion. Consider a device-to-device (D2D) communication scenario, where some users are transmitting some on-demand content locally cached in their devices using a common channel. Any reasonable multiple access scheme will ensure that two nearly users are never simultaneously active as they will cause severe mutual interference and thereby reducing the network-wide sum rate. Thus the active users in the network will have some spatial repulsion. The locations of these users can be modeled as determinantal point processes (DPPs). The key property of DPP is that it forms a bridge between stochastic geometry and machine learning, two otherwise non-overlapping paradigms for wireless network modeling and design. The main focus in this direction is to explore the learning framework of DPP and bring together advantages of stochastic geometry and machine learning to construct a new class of data-driven analytical network models.
Klimešová, Marie. "Stochastický kalkulus a jeho aplikace v biomedicínské praxi." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2019. http://www.nusl.cz/ntk/nusl-409091.
Full textBrown, Martin Lloyd. "Stochastic process approximation method with application to random volterra integral equations." Diss., Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/29222.
Full textKuntz, Georg Wolfgang Matthias. "Symbolic semantics and verification of stochastic process algebras." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=97894139X.
Full textVoskoglou, Michael Gr. "A Stochastic Model for the Process of Learning." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-81041.
Full textHaverinen, J. (Janne). "Adaptation through a Stochastic Evolutionary Neuron Migration Process." Doctoral thesis, University of Oulu, 2004. http://urn.fi/urn:isbn:9514273079.
Full textAndreou, Pantelis. "A random reordering stochastic process for regression residuals." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape10/PQDD_0003/NQ42492.pdf.
Full textWoodhead, Johnpaul. "Stochastic modelling of the cold forming nosing process." Thesis, University of Bristol, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.702148.
Full textMathur, Anup. "A stochastic process model for transient trace data." Diss., This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-10052007-143230/.
Full textCatalão, André Borges. "Modelagem estocástica de opções de câmbio no Brasil : aplicação de transformada rápida de Fourier e expansão assintótica ao modelo de Heston/." São Paulo : [s.n.], 2010. http://hdl.handle.net/11449/88592.
Full textBanca: Mario José de Oliveira
Banca: Marcos Eugênio da Silva
Resumo: Neste trabalho estudamos a calibração de opções de câmbio no mercado brasileiro utilizando o processo estocástico proposto por Heston [Heston, 1993], como uma alternativa ao modelo de apreçamento de Black e Scholes [Black e Scholes,1973], onde as volatilidades implícitas de opções para diferentes preços de exercícios e prazos são incorporadas ad hoc. Comparamos dois métodos de apreçamento: o método de Carr e Madan [Carr e Madan, 1999], que emprega transfomada rápida de Fourier e função característica, e expansão assintótica para baixos valores de volatilidade da variância. Com a nalidade de analisar o domínio de aplicabilidade deste método, selecionamos períodos de alta volatilidade no mercado, correspondente à crise subprime de 2008, e baixa volatilidade, correspondente ao período subsequente. Adicionalmente, estudamos a incorporação de swaps de variância para melhorar a calibração do modelo
Abstract: In this work we study the calibration of forex call options in the Brazilian market using the stochastic process proposed by Heston [Heston, 1993], as an alternative to the Black and Scholes [Black e Scholes,1973] pricing model, in which the implied option volatilities related to di erent strikes and maturities are incorporated in an ad hoc manner. We compare two pricing methods: one from Carr and Madan [Carr e Madan, 1999], which uses fast Fourier transform and characteristic function, and asymptotic expantion for low values of the volatility of variance. To analyze the applicability of this method, we select periods of high volatility in the market, related to the subprime crisis of 2008, and of low volatility, correspondent to the following period. In addition, we study the use of variance swaps to improve the calibration of the model
Mestre
Petersson, Mikael. "Perturbed discrete time stochastic models." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-128979.
Full textAt the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Manuscript. Paper 5: Manuscript. Paper 6: Manuscript.
Wei, Gang. "Modelling and inference for a class of doubly stochastic point processes." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260766.
Full textMane, Pranay P. "RO Process Optimization Based on Deterministic Process Model Coupled with Stochastic Cost Model." Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/14486.
Full textWong, Wee Chin. "Estimation and control of jump stochastic systems." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31775.
Full textCommittee Chair: Jay H. Lee; Committee Member: Alexander Gray; Committee Member: Erik Verriest; Committee Member: Magnus Egerstedt; Committee Member: Martha Grover; Committee Member: Matthew Realff. Part of the SMARTech Electronic Thesis and Dissertation Collection.
Popov, Roman [Verfasser]. "Process Development for Manufacturing Stochastic Peptide Microarrays / Roman Popov." Karlsruhe : KIT-Bibliothek, 2018. http://d-nb.info/1155474430/34.
Full textCavallin, Filippo <1988>. "Encoding G-Networks into the Stochastic Process Algebra PEPA." Master's Degree Thesis, Università Ca' Foscari Venezia, 2014. http://hdl.handle.net/10579/4328.
Full textKobulnická, Ivana. "Stochastické metódy v riadení portfólia." Master's thesis, Vysoká škola ekonomická v Praze, 2017. http://www.nusl.cz/ntk/nusl-359285.
Full textMüller, Jan. "Stochastic models and their solution in MS Excel." Master's thesis, Vysoká škola ekonomická v Praze, 2009. http://www.nusl.cz/ntk/nusl-17019.
Full textParida, Priyabrata. "Stochastic Geometry Perspective of Massive MIMO Systems." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/105089.
Full textDoctor of Philosophy
The emergence of cloud-based video and audio streaming services, online gaming platforms, instantaneous sharing of multimedia contents (e.g., photos, videos) through social networking platforms, and virtual collaborative workspace/meetings require the cellular communication networks to provide high data-rate as well as reliable and ubiquitous connectivity. These constantly evolving requirements can be met by designing a wireless network that harmoniously exploits the symbiotic co-existence among different types of cutting-edge wireless technologies. One such technology is massive multiple-input multiple-output (mMIMO), whose core idea is to equip the cellular base stations (BSs) with a large number of antennas that can be leveraged through appropriate signal processing algorithms to simultaneously accommodate multiple users with reduced network interference. For successful deployment of mMIMO in the upcoming cellular standards, i.e., fifth-generation (5G) and beyond systems, it is necessary to characterize its performance in a large-scale wireless network taking into account the inherent spatial randomness in the BS and user locations. To achieve this goal, in this dissertation, we propose different statistical methods for the performance analysis of mMIMO networks using tools from stochastic geometry, which is a field of mathematics related to the study of random patterns of points. One of the major deployment issues of mMIMO systems is pilot contamination, which is a form of coherent network interference that degrades user performance. The main reason behind pilot contamination is the reuse of pilot sequences, which are a finite number of known signal waveforms used for channel estimation between a user and its serving BS. Further, the effect of pilot contamination is more severe for the cell-edge users, which are farther from their own BSs. An efficient scheme to mitigate the effect of pilot contamination is fractional pilot reuse (FPR). However, the efficiency of this scheme depends on the pilot partitioning rule that decides the fraction of total pilot sequences that should be used by the cell-edge users. Using appropriate statistical constructs from the stochastic geometry literature, such as Johnson-Mehl cells, we present a partitioning rule for efficient implementation of the FPR scheme in a cellular mMIMO network. Next, we focus on the performance analysis of the cell-free mMIMO network. In contrast to the cellular network, where each user is served by a single BS, in a cell-free network each user can be served by multiple access points (APs), which have less complex hardware compared to a BS. Owing to this cooperative and distributed implementation, there are no cell-edge users. Similar to the cellular counterpart, the cell-free systems also suffer from pilot contamination due to the reuse of pilot sequences throughout the network. Inspired by a hardcore point process known as the random sequential adsorption (RSA) process, we develop a new distributed pilot assignment algorithm that mitigates the effect of pilot contamination by ensuring a minimum distance among the co-pilot users. Further, we show that the performance of this distributed pilot assignment scheme is appreciable compared to different centralized pilot assignment schemes, which are algorithmically more complex and difficult to implement in a network. Moreover, this pilot assignment scheme leads to the construction of a new point process, namely the multilayer RSA process. We derive the statistical properties of this point process both in one and two-dimensional spaces. Further, in a cell-free mMIMO network, the APs are connected to a centralized baseband unit (BBU) that performs the bulk of the signal processing operations through finite capacity links, such as fiber optic cables. Apart from pilot contamination, another implementational issue associated with the cell-free mMIMO systems is the finite capacity of fronthaul links that results in user performance degradation. Using appropriate stochastic geometry-based tools, we model and analyze this network for two different implementation scenarios. In the first scenario, we consider a finite network where each AP serves all the users in the network. In the second scenario, we consider an infinite network where each user is served by a few nearby APs. As a consequence of this user-centric implementation, for each user, the BBU only needs to communicate with fewer APs thereby reducing information load on fronthaul links. From our analyses, we propose key guidelines for the deployment of both types of scenarios. The type of mMIMO systems that are discussed in this work will be operated in the sub-6 GHz frequency range of the electromagnetic spectrum. Owing to the limited availability of spectrum resources, usually, spectrum sharing is encouraged among different cellular operators in such bands. One such example is the citizen broadband radio service (CBRS) spectrum sharing systems proposed by the Federal Communications Commission (FCC). The final contribution of this dissertation focuses on the potential improvement that is possible by the use of mMIMO in the CBRS systems. As our first step, using tools from stochastic geometry, we model and analyze this system with a single antenna at the BSs. In our model, we take into account the key guidelines by the FCC for co-existence between licensed and unlicensed operators. Leveraging properties of the Poisson hole process and hardcore process, we provide useful theoretical expressions for different performance metrics such as medium access probability, coverage probability, and area spectral efficiency. These results are used to obtain system design guidelines for successful co-existence between these networks. We further highlight the potential improvement in the user performance with multiple antennas at the unlicensed BS.
Roelly, Sylvie. "Reciprocal processes : a stochastic analysis approach." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6458/.
Full textChetlur, Ravi Vishnu Vardhan. "Stochastic Geometry for Vehicular Networks." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99954.
Full textDoctor of Philosophy
Vehicular communication networks are essential to the development of intelligent transportation systems (ITS) and improving road safety. As the in-vehicle sensors can assess only their immediate environment, vehicular nodes exchange information about critical events, such as accidents and sudden braking, with other vehicles, pedestrians, roadside infrastructure, and cellular base stations in order to make critical decisions in a timely manner. Considering the time-sensitive nature of this information, it is of paramount importance to design efficient communication networks that can support the exchange of this information with reliable and high-speed wireless links. Typically, prior to actual deployment, any design of a wireless network is subject to extensive analysis under various operational scenarios using computer simulations. However, it is not viable to rely entirely on simulations for the system design of highly complex systems, such as the vehicular networks. Hence, it is necessary to develop analytical methods that can complement simulators and also serve as a benchmark. One of the approaches that has gained popularity in the recent years for the modeling and analysis of large-scale wireless networks is the use of tools from stochastic geometry. In this approach, we endow the locations of wireless nodes with some distribution and analyze various aspects of the network by leveraging the properties of the distribution. Traditionally, wireless networks have been studied using simple spatial models in which the wireless nodes can lie anywhere on the domain of interest (often a 1D or a 2D plane). However, vehicular networks have a unique spatial geometry because the locations of vehicular nodes are restricted to roadways. Therefore, in order to model the locations of vehicular nodes in the network, we have to first model the underlying road systems. Further, we should also consider the randomness in the locations of vehicles on each road. So, we consider a doubly stochastic model called Poisson line Cox process (PLCP), in which the spatial layout of roads are modeled by random lines and the locations of vehicles on the roads are modeled by random set of points on these lines. As is usually the case in wireless networks, multiple vehicular nodes and roadside units (RSUs) operate at the same frequency due to the limited availability of radio frequency spectrum, which causes interference. Therefore, any receiver in the network obtains a signal that is a mixture of the desired signal from the intended transmitter and the interfering signals from the other transmitters. The ratio of the power of desired signal to the aggregate power of the interfering signals, which is called as the signal-to-interference ratio (SIR), depends on the locations of the transmitters with respect to the receiver. A receiver in the network is said to be in coverage if the SIR measured at the location of the receiver exceeds the required threshold to successfully decode the message. The probability of occurrence of this event is referred to as the coverage probability and it is one of the fundamental metrics that is used to characterize the performance of a wireless network. In our work, we have analytically characterized the coverage probability of the typical vehicular node in the network. This was the first work to present the coverage analysis of a vehicular network using the aforementioned doubly stochastic model. In addition to coverage probability, we have also explored other performance metrics such as data rate, which is the number of bits that can be successfully communicated per unit time, and spectral efficiency. Our analysis has revealed interesting trends in the coverage probability as a function of key system parameters such as the density of roads in a region (total length of roads per unit area), and the density of vehicles on the roads. We have shown that the vehicular nodes in areas with high density of roads have lower coverage than those in areas with sparsely distributed roads. On the other hand, the coverage probability of a vehicular node improves as the density of vehicles on the roads increases. Such insights are quite useful in the design and deployment of network infrastructure. While our research was primarily focused on communication networks, the utility of the spatial models considered in these works extends to other areas of engineering. For a special variant of the PLCP, we have derived the distribution of the shortest path distance between an arbitrary point and its nearest neighbor in the sense of path distance. The analytical framework developed in this work allows us to answer several important questions pertaining to infrastructure planning and personnel deployment.
Li, Zheng. "Approximation to random process by wavelet basis." View abstract/electronic edition; access limited to Brown University users, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3318378.
Full textLebre, Sophie. "Stochastic process analysis for Genomics and Dynamic Bayesian Networks inference." Phd thesis, Université d'Evry-Val d'Essonne, 2007. http://tel.archives-ouvertes.fr/tel-00260250.
Full textFirst we study a parsimonious Markov model called Mixture Transition Distribution (MTD) model which is a mixture of Markovian transitions. The overly high number of constraints on the parameters of this model hampers the formulation of an analytical expression of the Maximum Likelihood Estimate (MLE). We propose to approach the MLE thanks to an EM algorithm. After comparing the performance of this algorithm to results from the litterature, we use it to evaluate the relevance of MTD modeling for bacteria DNA coding sequences in comparison with standard Markovian modeling.
Then we propose two different approaches for genetic regulation network recovering. We model those genetic networks with Dynamic Bayesian Networks (DBNs) whose edges describe the dependency relationships between time-delayed genes expression. The aim is to estimate the topology of this graph despite the overly low number of repeated measurements compared with the number of observed genes.
To face this problem of dimension, we first assume that the dependency relationships are homogeneous, that is the graph topology is constant across time. Then we propose to approximate this graph by considering partial order dependencies. The concept of partial order dependence graphs, already introduced for static and non directed graphs, is adapted and characterized for DBNs using the theory of graphical models. From these results, we develop a deterministic procedure for DBNs inference.
Finally, we relax the homogeneity assumption by considering the succession of several homogeneous phases. We consider a multiple changepoint
regression model. Each changepoint indicates a change in the regression model parameters, which corresponds to the way an expression level depends on the others. Using reversible jump MCMC methods, we develop a stochastic algorithm which allows to simultaneously infer the changepoints location and the structure of the network within the phases delimited by the changepoints.
Validation of those two approaches is carried out on both simulated and real data analysis.
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