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Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering

Rong Situ

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No disponible.

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2005 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-25083-0

ISBN electrónico

978-0-387-25175-2

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer Science+Business Media, Inc. 2005

Tabla de contenidos

Martingale Theory and the Stochastic Integral for Point Processes

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part I - Stochastic Differential Equations with Jumps in | Pp. 3-38

Brownian Motion, Stochastic Integral and Ito's Formula

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part I - Stochastic Differential Equations with Jumps in | Pp. 39-74

Stochastic Differential Equations

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part I - Stochastic Differential Equations with Jumps in | Pp. 75-101

Some Useful Tools in Stochastic Differential Equations

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part I - Stochastic Differential Equations with Jumps in | Pp. 103-137

Stochastic Differential Equations with Non-Lipschitzian Coefficients

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part I - Stochastic Differential Equations with Jumps in | Pp. 139-160

How to Use the Stochastic Calculus to Solve SDE

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part II - Applications | Pp. 163-168

Linear and Non-linear Filtering

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part II - Applications | Pp. 169-204

Option Pricing in a Financial Market and BSDE

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part II - Applications | Pp. 205-275

Optimal Consumption by H-J-B Equation and Lagrange Method

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part II - Applications | Pp. 277-290

Comparison Theorem and Stochastic Pathwise Control

Rong Situ

In the previous chapters I described observational research projects that can be done using equipment that is commonly available in the amateur astronomer’s toolkit, or which can be added at modest expense. I avoided projects that require the use of math beyond standard high-school algebra. There are, of course, valuable projects that go outside these arbitrary boundaries. The purpose of this chapter is to identify additional projects that may be of interest to the amateur researcher. If you are willing to invest in some specialized equipment, or do some more complex math, then these projects can be brought within the boundaries of your universe. The equipment needed for some of them is likely to cost you a couple of thousand dollars, and may also require that you do some custom design, construction, and de-bugging. Depending on your budget and your enthusiasm for a particular area of research, these can be extremely rewarding investments in your hobby.

Part II - Applications | Pp. 291-327