Procesos Estoccsticos: El Proceso De Wiener (Stochastic Processes: The Wiener Process)

2013 ◽  
Author(s):  
Juan Mascareeas
Keyword(s):  
Stochastic Processes ◽  
Wiener Process

Evaluations of absorption probabilities for the Wiener process on large intervals

1980 ◽  
Vol 17 (02) ◽  
pp. 363-372 ◽  
Author(s):  
C. Park ◽  
F. J. Schuurmann
Keyword(s):  
Stochastic Processes ◽  
Wiener Process ◽  
Standard Wiener Process ◽  
Computationally Efficient ◽  
The Past ◽  
Gaussian Stochastic Processes ◽  
Absorption Probabilities

Let {W(t), 0≦t<∞} be the standard Wiener process. The computation schemes developed in the past are not computationally efficient for the absorption probabilities of the type P{sup0≦t≦T W(t) − f(t) ≧ 0} when either T is large or f(0) > 0 is small. This paper gives an efficient and accurate algorithm to compute such probabilities, and some applications to other Gaussian stochastic processes are discussed.

scholarly journals Optimal control of ultimately bounded stochastic processes

1974 ◽  
Vol 53 ◽  
pp. 157-170
Author(s):  
Yoshio Miyahara
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Markov Process ◽  
Stochastic Differential Equation ◽  
Stochastic Processes ◽  
Wiener Process ◽  
Admissible Control ◽  
Standard Wiener Process ◽  
The Cost

We shall consider the optimal control for a system governed by a stochastic differential equationwhere u(t, x) is an admissible control and W(t) is a standard Wiener process. By an optimal control we mean a control which minimizes the cost and in addition makes the corresponding Markov process stable.

Evaluations of absorption probabilities for the Wiener process on large intervals

1980 ◽  
Vol 17 (2) ◽  
pp. 363-372 ◽  
Author(s):  
C. Park ◽  
F. J. Schuurmann
Keyword(s):  
Stochastic Processes ◽  
Wiener Process ◽  
Standard Wiener Process ◽  
Computationally Efficient ◽  
The Past ◽  
Gaussian Stochastic Processes ◽  
Absorption Probabilities

Let {W(t), 0≦t<∞} be the standard Wiener process. The computation schemes developed in the past are not computationally efficient for the absorption probabilities of the type P{sup0≦t≦TW(t) − f(t) ≧ 0} when either T is large or f(0) > 0 is small. This paper gives an efficient and accurate algorithm to compute such probabilities, and some applications to other Gaussian stochastic processes are discussed.

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