scholarly journals On the first hitting place of the integrated Wiener process

1989 ◽  
Vol 21 (4) ◽  
pp. 945-948 ◽  
Author(s):  
Mario Lefebvre ◽  
Éric Léonard
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
Moment Generating Function ◽  
One Dimensional ◽  
The Moment

Let dx(t) = y(t) dt, where y(t) is a one-dimensional Wiener process. In this note, we obtain a formula for the moment-generating function of y(T), where T is the 1/2-winding time about the origin of the integrated Wiener process x(t).

scholarly journals First Passage Problems for Asymmetric Wiener Processes

2006 ◽  
Vol 43 (1) ◽  
pp. 175-184 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
Expected Value ◽  
First Passage ◽  
One Dimensional ◽  
Wiener Processes ◽  
The Moment

The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.

scholarly journals First Passage Problems for Asymmetric Wiener Processes

2006 ◽  
Vol 43 (01) ◽  
pp. 175-184
Author(s):  
Mario Lefebvre
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
Expected Value ◽  
First Passage ◽  
One Dimensional ◽  
Wiener Processes ◽  
The Moment

The problem of computing the moment generating function of the first passage time T to a &gt; 0 or −b &lt; 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.

scholarly journals On the first hitting place of the integrated Wiener process

1989 ◽  
Vol 21 (04) ◽  
pp. 945-948
Author(s):  
Mario Lefebvre ◽  
Éric Léonard
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
Moment Generating Function ◽  
One Dimensional ◽  
The Moment

Let dx(t) = y(t) dt, where y(t) is a one-dimensional Wiener process. In this note, we obtain a formula for the moment-generating function of y(T), where T is the 1/2-winding time about the origin of the integrated Wiener process x(t).

scholarly journals The ruin problem for a Wiener process with state-dependent jumps

2020 ◽  
Vol 16 (1) ◽  
pp. 13-23
Author(s):  
M. Lefebvre
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Diffusion Process ◽  
Wiener Process ◽  
Jump Diffusion ◽  
Moment Generating Function ◽  
Continuous Part ◽  
State Dependent ◽  
The Moment ◽  
First Time

AbstractLet X(t) be a jump-diffusion process whose continuous part is a Wiener process, and let T (x) be the first time it leaves the interval (0,b), where x = X(0). The jumps are negative and their sizes depend on the value of X(t). Moreover there can be a jump from X(t) to 0. We transform the integro-differential equation satisfied by the probability p(x) := P[X(T (x)) = 0] into an ordinary differential equation and we solve this equation explicitly in particular cases. We are also interested in the moment-generating function of T (x).

scholarly journals A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 453 ◽  
Author(s):  
Mukhtar ◽  
Sohaib ◽  
Ahmad
Keyword(s):  
Numerical Approximation ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Moment Generating Function ◽  
Numerical Approach ◽  
Test Problems ◽  
Batch Crystallization ◽  
One Dimensional ◽  
Engineering Sciences ◽  
The Moment

In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the efficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.

Problèmes de premier passage résolubles par la méthode de séparation des variables

1995 ◽  
Vol 32 (02) ◽  
pp. 337-348
Author(s):  
Mario Lefebvre
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Generating Function ◽  
Moment Generating Function ◽  
First Passage Times ◽  
Standard Brownian Motion ◽  
First Passage ◽  
The Moment ◽  
Passage Times

In this paper, bidimensional stochastic processes defined by ax(t) = y(t)dt and dy(t) = m(y)dt + [2v(y)]1/2 dW(t), where W(t) is a standard Brownian motion, are considered. In the first section, results are obtained that allow us to characterize the moment-generating function of first-passage times for processes of this type. In Sections 2 and 5, functions are computed, first by fixing the values of the infinitesimal parameters m(y) and v(y) then by the boundary of the stopping region.

scholarly journals Mellin’s Transform and Application to Some Time Series Models

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
S. S. Appadoo ◽  
A. Thavaneswaran ◽  
S. Mandal
Keyword(s):  
Time Series ◽  
Generating Function ◽  
Mellin Transform ◽  
Fuzzy Numbers ◽  
Moment Generating Function ◽  
Time Series Models ◽  
Form Expression ◽  
The Moment ◽  
Close Form ◽  
Skewness And Kurtosis

This paper uses the Mellin transform to establish the means, variances, skewness, and kurtosis of fuzzy numbers and applied them to the random coefficient autoregressive (RCA) time series models. We also give a close form expression to the moment generating function related to fuzzy numbers. It is shown that the results of the proposed time series models are consistent with those of the conventional time series models and that the developed concepts are straightforward and easily implemented.

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