scholarly journals Approximation of Expectation of Diffusion Process and Mathematical Finance

2018 ◽  
Author(s):  
Shigeo Kusuoka
Keyword(s):  
Diffusion Process ◽  
Mathematical Finance

scholarly journals On the Monitoring Error of the Supremum of a Normal Jump Diffusion Process

2011 ◽  
Vol 48 (4) ◽  
pp. 1021-1034 ◽  
Author(s):  
Ao Chen ◽  
Liming Feng ◽  
Renming Song
Keyword(s):  
Brownian Motion ◽  
Diffusion Process ◽  
Riemann Zeta Function ◽  
Time Horizon ◽  
Jump Diffusion ◽  
Mathematical Finance ◽  
The Riemann Zeta Function ◽  
Jump Diffusion Process ◽  
Riemann Zeta ◽  
Finite Time Horizon

We derive an expansion for the (expected) difference between the continuously monitored supremum and evenly monitored discrete maximum over a finite time horizon of a jump diffusion process with independent and identically distributed normal jump sizes. The monitoring error is of the form a0 / N1/2 + a1 / N3/2 + · · · + b1 / N + b2 / N2 + b4 / N4 + · · ·, where N is the number of monitoring intervals. We obtain explicit expressions for the coefficients {a0, a1, …, b1, b2, …}. In particular, a0 is proportional to the value of the Riemann zeta function at ½, a well-known fact that has been observed for Brownian motion in applied probability and mathematical finance.

scholarly journals On the Monitoring Error of the Supremum of a Normal Jump Diffusion Process

2011 ◽  
Vol 48 (04) ◽  
pp. 1021-1034 ◽  
Author(s):  
Ao Chen ◽  
Liming Feng ◽  
Renming Song
Keyword(s):  
Brownian Motion ◽  
Diffusion Process ◽  
Riemann Zeta Function ◽  
Time Horizon ◽  
Jump Diffusion ◽  
Mathematical Finance ◽  
The Riemann Zeta Function ◽  
Jump Diffusion Process ◽  
Riemann Zeta ◽  
Finite Time Horizon

We derive an expansion for the (expected) difference between the continuously monitored supremum and evenly monitored discrete maximum over a finite time horizon of a jump diffusion process with independent and identically distributed normal jump sizes. The monitoring error is of the forma0/N1/2+a1/N3/2+ · · · +b1/N+b2/N2+b4/N4+ · · ·, whereNis the number of monitoring intervals. We obtain explicit expressions for the coefficients {a0,a1, …,b1,b2, …}. In particular,a0is proportional to the value of the Riemann zeta function at ½, a well-known fact that has been observed for Brownian motion in applied probability and mathematical finance.

Burgers fluid flow in perspective of Buongiorno’s model with improved heat and mass flux theory for stretching cylinder

2020 ◽  
Vol 92 (3) ◽  
pp. 31101
Author(s):  
Zahoor Iqbal ◽  
Masood Khan ◽  
Awais Ahmed
Keyword(s):  
Diffusion Process ◽  
Mathematical Formulation ◽  
Thermal Relaxation ◽  
Mass Diffusion ◽  
Stretching Cylinder ◽  
Discussion Section ◽  
Buongiorno’S Model ◽  
Homotopy Analysis ◽  
Burgers Fluid ◽  
Diffusion Phenomena

In this study, an effort is made to model the thermal conduction and mass diffusion phenomena in perspective of Buongiorno’s model and Cattaneo-Christov theory for 2D flow of magnetized Burgers nanofluid due to stretching cylinder. Moreover, the impacts of Joule heating and heat source are also included to investigate the heat flow mechanism. Additionally, mass diffusion process in flow of nanofluid is examined by employing the influence of chemical reaction. Mathematical modelling of momentum, heat and mass diffusion equations is carried out in mathematical formulation section of the manuscript. Homotopy analysis method (HAM) in Wolfram Mathematica is utilized to analyze the effects of physical dimensionless constants on flow, temperature and solutal distributions of Burgers nanofluid. Graphical results are depicted and physically justified in results and discussion section. At the end of the manuscript the section of closing remarks is also included to highlight the main findings of this study. It is revealed that an escalation in thermal relaxation time constant leads to ascend the temperature curves of nanofluid. Additionally, depreciation is assessed in mass diffusion process due to escalating amount of thermophoretic force constant.

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Adjoint Operator ◽  
Integral Kernel ◽  
Mathematical Finance ◽  
Elliptic Operators ◽  
Complete Analysis ◽  
Time Behavior ◽  
Degenerate Elliptic Operators ◽  
Regularity Properties ◽  
Degenerate Elliptic ◽  
Mathematical Foundations

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

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