Small Noise Approximations for Diffusion Processes

2008 ◽  
pp. 169-184
Author(s):  
Crispin Gardiner
Keyword(s):  
Diffusion Processes ◽  
Small Noise

scholarly journals Nonasymptotic performance analysis of importance sampling schemes for small noise diffusions

2015 ◽  
Vol 52 (03) ◽  
pp. 797-810 ◽  
Author(s):  
Konstantinos Spiliopoulos
Keyword(s):  
Asymptotic Expansion ◽  
Importance Sampling ◽  
Diffusion Processes ◽  
Correction Term ◽  
Poor Performance ◽  
Change Of Measure ◽  
Small Noise ◽  
Second Moment ◽  
Sampling Schemes ◽  
Accurate Comparison

In this paper we develop a prelimit analysis of performance measures for importance sampling schemes related to small noise diffusion processes. In importance sampling the performance of any change of measure is characterized by its second moment. For a given change of measure, we characterize the second moment of the corresponding estimator as the solution to a partial differential equation, which we analyze via a full asymptotic expansion with respect to the size of the noise and obtain a precise statement on its accuracy. The main correction term to the decay rate of the second moment solves a transport equation that can be solved explicitly. The asymptotic expansion that we obtain identifies the source of possible poor performance of nevertheless asymptotically optimal importance sampling schemes and allows for a more accurate comparison among competing importance sampling schemes.

Large time and small noise asymptotic results for mean reverting diffusion processes with applications

2000 ◽  
Vol 16 (2) ◽  
pp. 401-419 ◽  
Author(s):  
Jeffrey Callen ◽  
Suresh Govindaraj ◽  
Lin Xu
Keyword(s):  
Large Time ◽  
Diffusion Processes ◽  
Asymptotic Results ◽  
Small Noise

scholarly journals Nonasymptotic performance analysis of importance sampling schemes for small noise diffusions

2015 ◽  
Vol 52 (3) ◽  
pp. 797-810 ◽  
Author(s):  
Konstantinos Spiliopoulos
Keyword(s):  
Asymptotic Expansion ◽  
Importance Sampling ◽  
Diffusion Processes ◽  
Correction Term ◽  
Poor Performance ◽  
Change Of Measure ◽  
Small Noise ◽  
Second Moment ◽  
Sampling Schemes ◽  
Accurate Comparison

In this paper we develop a prelimit analysis of performance measures for importance sampling schemes related to small noise diffusion processes. In importance sampling the performance of any change of measure is characterized by its second moment. For a given change of measure, we characterize the second moment of the corresponding estimator as the solution to a partial differential equation, which we analyze via a full asymptotic expansion with respect to the size of the noise and obtain a precise statement on its accuracy. The main correction term to the decay rate of the second moment solves a transport equation that can be solved explicitly. The asymptotic expansion that we obtain identifies the source of possible poor performance of nevertheless asymptotically optimal importance sampling schemes and allows for a more accurate comparison among competing importance sampling schemes.

Meridional Circulation, Turbulence, and Diffusion Processes in Stars

1976 ◽  
Vol 32 ◽  
pp. 109-116 ◽  
Author(s):  
S. Vauclair
Keyword(s):  
Convection Zone ◽  
Diffusion Processes ◽  
Meridional Circulation ◽  
Diffusion Time ◽  
Work In Progress ◽  
First Results ◽  
Stellar Envelopes ◽  
And Diffusion ◽  
Turbulence And Diffusion ◽  
Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

Ergodic Control of Diffusion Processes

2009 ◽  
Author(s):  
Ari Arapostathis ◽  
Vivek S. Borkar ◽  
Mrinal K. Ghosh
Keyword(s):  
Diffusion Processes ◽  
Ergodic Control

NMR-Study of Structure and Diffusion Processes in Li3N

1980 ◽  
Vol 41 (C6) ◽  
pp. C6-28-C6-31 ◽  
Author(s):  
R. Messer ◽  
H. Birli ◽  
K. Differt
Keyword(s):  
Diffusion Processes ◽  
Nmr Study ◽  
And Diffusion
Sign in / Sign up

Export Citation Format

Share Document