Titlebook: Brownian Motion, Martingales, and Stochastic Calculus; Jean-François Le Gall Textbook 2016 Springer International Publishing Switzerland 2

宴会

Filtrations and Martingales,eralize several notions introduced in the previous chapter in the framework of Brownian motion, and we provide a thorough discussion of stopping times. In a second step, we develop the theory of continuous time martingales, and, in particular, we derive regularity results for sample paths of marting

SMART

Continuous Semimartingales,gration in the next chapter. By definition, a continuous semimartingale is the sum of a continuous local martingale and a (continuous) finite variation process. In the present chapter, we study separately these two classes of processes. We start with some preliminaries about deterministic functions

Hypomania

flourish

General Theory of Markov Processes,a fundamental class of stochastic processes, with many applications in real life problems outside mathematics. The reason why Markov processes are so important comes from the so-called Markov property, which enables many explicit calculations that would be intractable for more general random process

Mundane

证明无罪

Stochastic Differential Equations,initions, we provide a detailed treatment of the Lipschitz case, where strong existence and uniqueness statements hold. Still in the Lipschitz case, we show that the solution of a stochastic differential equation is a Markov process with a Feller semigroup, whose generator is a second-order differen