On the Filtering Equations of a Multidimensional Diffusion Process (Increasing Coefficients)

1989 ◽  
Vol 33 (3) ◽  
pp. 574-578
Author(s):  
O. G. Purtukhiya
2020 ◽  
Vol 52 (1) ◽  
pp. 173-212
Author(s):  
Joris Bierkens ◽  
Frank van der Meulen ◽  
Moritz Schauer

AbstractSuppose X is a multidimensional diffusion process. Assume that at time zero the state of X is fully observed, but at time $T>0$ only linear combinations of its components are observed. That is, one only observes the vector $L X_T$ for a given matrix L. In this paper we show how samples from the conditioned process can be generated. The main contribution of this paper is to prove that guided proposals, introduced in [35], can be used in a unified way for both uniformly elliptic and hypo-elliptic diffusions, even when L is not the identity matrix. This is illustrated by excellent performance in two challenging cases: a partially observed twice-integrated diffusion with multiple wells and the partially observed FitzHugh–Nagumo model.


2000 ◽  
Vol 37 (1) ◽  
pp. 246-251 ◽  
Author(s):  
S. Balaji ◽  
S. Ramasubramanian

Let τr denote the hitting time of B(0:r) for a multidimensional diffusion process. We give verifiable criteria for finiteness/infiniteness of As an application we exhibit classes of diffusion processes which are recurrent but is infinite for all p > 0, |x| > r > 0; this includes the two-dimensional Brownian motion and the reflecting Brownian motion in a wedge with a certain parameter α = 0.


2000 ◽  
Vol 37 (01) ◽  
pp. 246-251 ◽  
Author(s):  
S. Balaji ◽  
S. Ramasubramanian

Let τ r denote the hitting time of B(0:r) for a multidimensional diffusion process. We give verifiable criteria for finiteness/infiniteness of As an application we exhibit classes of diffusion processes which are recurrent but is infinite for all p > 0, |x| > r > 0; this includes the two-dimensional Brownian motion and the reflecting Brownian motion in a wedge with a certain parameter α = 0.


2020 ◽  
Vol 92 (3) ◽  
pp. 31101
Author(s):  
Zahoor Iqbal ◽  
Masood Khan ◽  
Awais Ahmed

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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