Tài liệu RandomProcess2 pdf

Lecture 2

Stochastic Processes

2.1 Introduction

Spectral analysis is the study of models of a class called stationary stochastic

processes.

Stochastic processes {X(t) : t ∈ T} is a family or rv’s indexed by a variable t,

where t is a subset of T which may be infinite.

continuous → X(t)

discrete → Xt







These may be real, vector valued or

complex with suitable added indices.

We will use the Riemann-Stieltjes notation in what follows because mixed

continuous- discrete distributions are common for time series, and hence the R-S

notation is standard in stochastic theory. Let g(x) and H(x) be real valued func￾tions on [L, U] where L < U and L, U may be −∞, ∞ with suitable limiting

processes. Let PN be a partition of [L, U] into N + 1 intervals

L = x0 < x1 · · · < xN = U

Define the mesh fineness:

|PN | = max {x1 − x0, x2 − x1, . . . , xN − xN−1}

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