Titlebook: Stochastic Calculus; An Introduction Thro Paolo Baldi Textbook 2017 Springer International Publishing AG 2017 stochastic calculus.stochasti

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Stochastic Differential Equations,t. 9.8 we obtain some .. estimates that will allow us to specify the regularity of the paths and the dependence from the initial conditions. In the last sections we shall see that the solution of a stochastic differential equation is a Markov process and even a diffusion associated to a differential operator that we shall specify.

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Stochastic Processes,A stochastic process is a mathematical object that is intended to model the evolution in time of a random phenomenon. As will become clear in the sequel the appropriate setting is the following.

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Brownian Motion,Brownian motion is a particular stochastic process which is the prototype of the class of processes which will be our main concern. Its investigation is the object of this chapter.

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Martingales,Martingales are stochastic processes that enjoy many important, sometimes surprising, properties. When studying a process ., it is always a good idea to look for martingales “associated” to ., in order to take advantage of these properties.

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Markov Processes,In this chapter we introduce an important family of stochastic processes. Diffusions, which are the object of our investigation in the subsequent chapters, are instances of Markov processes.

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Stochastic Calculus,A process admitting a stochastic differential is called an .. An Ito process is therefore the sum of a process with finite variation and of a local martingale.