On Integral of a Semi-Markov Diffusion Process

2018 ◽  
Vol 229 (6) ◽  
pp. 782-791
Author(s):  
B. P. Harlamov
Keyword(s):  
Diffusion Process ◽  
Markov Diffusion

DRIFT TRANSFORMATIONS OF SYMMETRIC DIFFUSIONS, AND DUALITY

2007 ◽  
Vol 10 (04) ◽  
pp. 613-631 ◽  
Author(s):  
P. J. FITZSIMMONS
Keyword(s):  
Diffusion Process ◽  
Dirichlet Form ◽  
Infinitesimal Generator ◽  
Probabilistic Approach ◽  
Additive Functionals ◽  
Excessive Measure ◽  
Girsanov’S Theorem ◽  
Markov Diffusion ◽  
Symmetry Measure

Starting with a symmetric Markov diffusion process X (with symmetry measure m and L2 (m) infinitesimal generator A) and a suitable core [Formula: see text] for the Dirichlet form of X, we describe a class of derivations defined on [Formula: see text]. Associated with each such derivation B is a drift transformation of X, obtained through Girsanov's theorem. The transformed process XB is typically non-symmetric, but we are able to show that if the "divergence" of B is positive, then m is an excessive measure for XB, and the L2 (m) infinitesimal generator of XB is an extension of f ↦ Af + B (f). The methods used are mainly probabilistic, and involve the notions of even and odd continuous additive functionals, and Nakao's stochastic divergence. These methods yield a probabilistic approach to the adjoint of the semigroup of XB, and in particular lead to a solution of a problem of W. Stannat.

Comparison results for diffusions conditioned on positivity

1983 ◽  
Vol 20 (4) ◽  
pp. 766-777 ◽  
Author(s):  
Martin V. Day
Keyword(s):  
Diffusion Process ◽  
Conditional Probability ◽  
Comparison Theorem ◽  
Markov Diffusion ◽  
Comparison Results ◽  
Conditioned Diffusion ◽  
Initial Process

We consider a diffusion process on the reals subject to the conditional probability that the process is positive from t = 0 to the present. We establish comparison results between the conditioned diffusion and a second unconditioned Markov diffusion. One result allows the initial process to be non-Markov before conditioning. A stronger comparison theorem is shown to hold in the Markov case.

Comparison results for diffusions conditioned on positivity

1983 ◽  
Vol 20 (04) ◽  
pp. 766-777
Author(s):  
Martin V. Day
Keyword(s):  
Diffusion Process ◽  
Conditional Probability ◽  
Comparison Theorem ◽  
Markov Diffusion ◽  
Comparison Results ◽  
Conditioned Diffusion ◽  
Initial Process

We consider a diffusion process on the reals subject to the conditional probability that the process is positive from t = 0 to the present. We establish comparison results between the conditioned diffusion and a second unconditioned Markov diffusion. One result allows the initial process to be non-Markov before conditioning. A stronger comparison theorem is shown to hold in the Markov case.

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.

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