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The book discusses a class of discrete time stochastic growth processes for which the growth rate is proportional to the exponential of a Gaussian Markov process. These growth processes appear naturally in problems of mathematical finance as discrete time approximations of stochastic volatility models and stochastic interest rates models such as the Black-Derman-Toy and Black-Karasinski models. These processes can be mapped to interacting one-dimensional lattice gases with long-range interactions. The book gives a detailed discussion of these statistical mechanics models, including new results not available in the literature, and their implication for the stochastic growth models. The statistical mechanics analogy is used to understand observed non-analytic dependence of the Lyapunov exponents of the stochastic growth processes considered, which is related to phase transitions in the lattice gas system. The theoretical results are applied to simulations of financial models and are illustrated with Mathematica code. The book includes a general introduction to exponential stochastic growth with examples from biology, population dynamics and finance. The presentation does not assume knowledge of mathematical finance. The new results on lattice gases can be read independently of the rest of the book. The book should be useful to practitioners and academics studying the simulation and application of stochastic growth models.

Classical mechanics. Field theory --- Statistical physics --- statica (fysica) --- statistiek --- fysica --- Markov processes. --- Processos de Markov

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R (Computer program language) --- GNU-S (Computer program language) --- Domain-specific programming languages --- Processos de Markov --- R (Llenguatge de programació)

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Processos de Markov --- R (Llenguatge de programació) --- Llenguatges de programació --- GNU-S (Llenguatge de programació) --- Processos estocàstics --- Moviment brownià --- Processos de difusió --- Processos de moviment brownià --- R (Computer program language) --- GNU-S (Computer program language) --- Domain-specific programming languages

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This book deals with selected problems of machine perception, using various 2D and 3D imaging sensors. It proposes several new original methods, and also provides a detailed state-of-the-art overview of existing techniques for automated, multi-level interpretation of the observed static or dynamic environment. To ensure a sound theoretical basis of the new models, the surveys and algorithmic developments are performed in well-established Bayesian frameworks. Low level scene understanding functions are formulated as various image segmentation problems, where the advantages of probabilistic inference techniques such as Markov Random Fields (MRF) or Mixed Markov Models are considered. For the object level scene analysis, the book mainly relies on the literature of Marked Point Process (MPP) approaches, which consider strong geometric and prior interaction constraints in object population modeling. In particular, key developments are introduced in the spatial hierarchical decomposition of the observed scenarios, and in the temporal extension of complex MRF and MPP models. Apart from utilizing conventional optical sensors, case studies are provided on passive radar (ISAR) and Lidar-based Bayesian environment perception tasks. It is shown, via several experiments, that the proposed contributions embedded into a strict mathematical toolkit can significantly improve the results in real world 2D/3D test images and videos, for applications in video surveillance, smart city monitoring, autonomous driving, remote sensing, and optical industrial inspection.

Statistical science --- Mathematical statistics --- Probability theory --- Computer. Automation --- Geography --- computervisie --- GIS (geografisch informatiesysteem) --- waarschijnlijkheidstheorie --- statistiek --- statistisch onderzoek --- Markov processes. --- Bayesian statistical decision theory. --- Reconeixement de formes (Informàtica) --- Visió per ordinador --- Models matemàtics --- Processos de Markov --- Estadística bayesiana

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Convolutions (Mathematics) --- Differential operators. --- Diffusion processes. --- Markov processes --- Operators, Differential --- Differential equations --- Operator theory --- Convolution transforms --- Transformations, Convolution --- Distribution (Probability theory) --- Functions --- Integrals --- Transformations (Mathematics) --- Convolucions (Matemàtica) --- Operadors diferencials --- Processos de difusió --- Processos de Markov --- Teoria d'operadors --- Geometria espectral --- Operador de Schrödinger --- Transformacions de convolució --- Transformades de convolució --- Distribució (Teoria de la probabilitat) --- Funcions --- Transformacions (Matemàtica)