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Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-

Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-

The first half of Assurbanipal’s long reign (668–ca. 630 BCE) was a time of peace and great prosperity and political success for Assyria. But towards the middle of his reign a serious cris

The first half of Assurbanipal’s long reign (668–ca. 630 BCE) was a time of peace and great prosperity and political success for Assyria. But towards the middle of his reign a serious cris

Metapsychological Perspectives on Psychic Survival explores the integration of traumatic helplessness in the course of psychoanalytic treatment. Based on the author’s many years of experience of worki

Metapsychological Perspectives on Psychic Survival explores the integration of traumatic helplessness in the course of psychoanalytic treatment. Based on the author’s many years of experience of worki

In a word-drunk romp through an alternate, pre-apocalyptic United States, Ana Simo’s fiction debut, Heartland, is the uproarious story of a thwarted writer’s elaborate revenge on the woman

The internal stability and cohesion of the Neo-Assyrian Empire to a very considerable degree rested on the public image of the King as an omnipotent earthly representative of God. Many elaborate ritua

The internal stability and cohesion of the Neo-Assyrian Empire to a very considerable degree rested on the public image of the King as an omnipotent earthly representative of God. Many elaborate ritua

Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book's practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include Matlab computations, and the numerous end-of-chapter exercises include