Stochastic Differential Equations: Basics and Applications

Tony G. Deangelo (Editor)

Series: Mathematics Research Developments
BISAC: MAT029040




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In this collection, the authors begin by introducing a methodology for examining continuous-time Ornstein-Uhlenbech family processes defined by stochastic differential equations (SDEs). Additionally, a study is presented introducing the mathematics of mixed effect parameters in univariate and bivariate SDEs and describing how such a model can be used to aid our understanding of growth processes using real world datasets.

Results and experience from applying the concepts and techniques in an extensive individual tree and stand growth modeling program in Lithuania are described as examples. Next, the authors present a review paper on J-calculus, as well as a contributed paper which displays some new results on the topic and deepens some special properties in relation with non-differentiability of functions.

Following this, this book develops the general framework to be used in our papers [2, 9, 8]. The starting point for the discussion will be the standard risk-sensitive structures, and how constructions of this kind can be given a rigorous treatment. The risk-sensitive optimal control is also investigated by using the extending part of this of problem of backward stochastic equation. In the closing article, the authors note that the square of an O-U process is the Cox-Ingersoll-Ross process used as a model for volatility in finance. The filtered form of the original hazard rate based on this new observation is also studied. If the difference between the original hazard rate and the filtered one is not significant, then the person is not affected by the new frailty.


Chapter 1. Univariate and Bivariate Diffusion Models: Computational Aspects and Applications to Forestry
(Petras Rupšys, PhD, Centre of Mathematics, Physics and Information Technologies, Aleksandras Stulginskis University, Kaunas, Lithuania)

Chapter 2. Towards a New Class of Pseudo-Stochastic Differential Equations Driven by the Weierstrass Function
(Guy Jumarie, Department of Mathematics, University of Québec at Montréal, Montreal, QC, Canada)

Chapter 3. The Use of Girsanov's Theorem to Describe the Risk-Sensitive Problem and Application to Optimal Control
(Adel Chala; Dahbia Hafayeda and Rania Khallout, Laboratory of Applied Mathematics, Mohamed Khider University, Biskra, Algeria)

Chapter 4. Hazard Rate under Frailty
(V. Mandrekar and U. V. Naik-Nimbalkar, Department of Statistics and Probability, Michigan State University, East Lansing, US)


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