Time reversal of diffusion processes

2005 ◽  
pp. 176-182
Author(s):  
U. G. Haussmann ◽  
E. Pardoux
Keyword(s):  
Time Reversal ◽  
Diffusion Processes

scholarly journals Time reversal of diffusion processes with a boundary condition

1988 ◽  
Vol 28 (2) ◽  
pp. 275-292 ◽  
Author(s):  
Patrick Cattiaux
Keyword(s):  
Boundary Condition ◽  
Time Reversal ◽  
Diffusion Processes

scholarly journals Integration by Parts and Time Reversal for Diffusion Processes

1989 ◽  
Vol 17 (1) ◽  
pp. 208-238 ◽  
Author(s):  
A. Millet ◽  
D. Nualart ◽  
M. Sanz
Keyword(s):  
Time Reversal ◽  
Diffusion Processes ◽  
Integration By Parts

Duality and Time Reversal of Diffusion Processes

1993 ◽  
pp. 55-88
Author(s):  
Masao Nagasawa
Keyword(s):  
Time Reversal ◽  
Diffusion Processes

Diffusion processes on an open time interval and their time reversal

1996 ◽  
pp. 261-280 ◽  
Author(s):  
Masao Nagasawa ◽  
Thomas Domenig
Keyword(s):  
Time Reversal ◽  
Diffusion Processes ◽  
Time Interval ◽  
Open Time

scholarly journals Time reversal of some stationary jump diffusion processes from population genetics

2010 ◽  
Vol 42 (4) ◽  
pp. 1147-1171
Author(s):  
Martin Hutzenthaler ◽  
Jesse Earl Taylor
Keyword(s):  
Population Genetics ◽  
Genetic Variation ◽  
Local Time ◽  
Time Reversal ◽  
Boundary Point ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Jump Diffusion Processes ◽  
Forward Diffusion ◽  
Forward Process

We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.

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