A Generalized Taylor–Aris Formula and Skew Diffusion

2006 ◽  
Vol 5 (3) ◽  
pp. 786-801 ◽  
Author(s):  
Jorge M. Ramirez ◽  
Enrique A. Thomann ◽  
Edward C. Waymire ◽  
Roy Haggerty ◽  
Brian Wood
Keyword(s):  
Skew Diffusion

First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes

2009 ◽  
Vol 16 (04) ◽  
pp. 325-350 ◽  
Author(s):  
Mario Abundo
Keyword(s):  
Diffusion Process ◽  
Diffusion Processes ◽  
Exit Time ◽  
Skew Brownian Motion ◽  
One Dimensional ◽  
Mean Exit Time ◽  
The Mean ◽  
The Right ◽  
Analytical Expressions ◽  
Skew Diffusion

For a, b > 0, we consider a temporally homogeneous, one-dimensional diffusion process X(t) defined over I = (-b, a), with infinitesimal parameters depending on the sign of X(t). We suppose that, when X(t) reaches the position 0, it is reflected rightward to δ with probability p > 0 and leftward to -δ with probability 1 - p, where δ > 0. Closed analytical expressions are found for the mean exit time from the interval (-b, a), and for the probability of exit through the right end a, in the limit δ → 0+, generalizing the results of Lefebvre, holding for asymmetric Wiener process. Moreover, in alternative to the heavy analytical calculations, a numerical method is presented to estimate approximately the quantities above. Furthermore, on the analogy of skew Brownian motion, the notion of skew diffusion process is introduced. Some examples and numerical results are also reported.

scholarly journals On the weak approximation of a skew diffusion by an Euler-type scheme

Bernoulli ◽  
2018 ◽  
Vol 24 (3) ◽  
pp. 1653-1691 ◽  
Author(s):  
Noufel Frikha
Keyword(s):  
Weak Approximation ◽  
Skew Diffusion
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