scholarly journals Uniqueness of solution to the Kolmogorov forward equation: applications to white noise theory of filtering

2010 ◽  
Vol 4 (1) ◽  
Author(s):  
Abhay G Bhatt ◽  
Rajeeva L Karandikar
Keyword(s):  
White Noise ◽  
Uniqueness Of Solution ◽  
Forward Equation ◽  
Kolmogorov Forward Equation

scholarly journals Multinomial approximation to the Kolmogorov Forward Equation for jump (population) processes

2018 ◽  
Vol 5 (1) ◽  
pp. 1556192 ◽  
Author(s):  
Mario A. Natiello ◽  
Raúl H. Barriga ◽  
Marcelo Otero ◽  
Hernán G. Solari ◽  
Yuriy Rogovchenko
Keyword(s):  
Forward Equation ◽  
Kolmogorov Forward Equation ◽  
Population Processes

Controllability and decentralized stabilization of the Kolmogorov forward equation for Markov chains

Automatica ◽  
2021 ◽  
Vol 124 ◽  
pp. 109351
Author(s):  
Karthik Elamvazhuthi ◽  
Shiba Biswal ◽  
Spring Berman
Keyword(s):  
Markov Chains ◽  
Decentralized Stabilization ◽  
Forward Equation ◽  
Kolmogorov Forward Equation

scholarly journals From Bachelier to Dupire via optimal transport

2021 ◽  
Vol 26 (1) ◽  
pp. 59-84
Author(s):  
Mathias Beiglböck ◽  
Gudmund Pammer ◽  
Walter Schachermayer
Keyword(s):  
Optimal Transport ◽  
Formal Solution ◽  
Mathematical Finance ◽  
Forward Equation ◽  
Survey Article ◽  
Formal Derivation ◽  
Kolmogorov Forward Equation ◽  
Free Model ◽  
Volatility Surface ◽  
Phd Thesis

AbstractFamously, mathematical finance was started by Bachelier in his 1900 PhD thesis where – among many other achievements – he also provided a formal derivation of the Kolmogorov forward equation. This also forms the basis for Dupire’s (again formal) solution to the problem of finding an arbitrage-free model calibrated to a given volatility surface. The latter result has rigorous counterparts in the theorems of Kellerer and Lowther. In this survey article, we revisit these hallmarks of stochastic finance, highlighting the role played by some optimal transport results in this context.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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