scholarly journals Characterizing the path-independence of the Girsanov transformation for non-Lipschitz SDEs with jumps

2016 ◽  
Vol 119 ◽  
pp. 326-333 ◽  
Author(s):  
Huijie Qiao ◽  
Jiang-Lun Wu
Keyword(s):  
Girsanov Transformation ◽  
Path Independence

scholarly journals Space-distribution PDEs for path independent additive functionals of McKean–Vlasov SDEs

2020 ◽  
Vol 23 (03) ◽  
pp. 2050018
Author(s):  
Panpan Ren ◽  
Feng-Yu Wang
Keyword(s):  
Product Space ◽  
Space Variable ◽  
Space Distribution ◽  
Nonlinear Pdes ◽  
Probability Measures ◽  
Girsanov Transformation ◽  
Additive Functionals ◽  
Drift Term ◽  
Path Independence ◽  
Girsanov Transformations

Let [Formula: see text] be the space of probability measures on [Formula: see text] with finite second moment. The path independence of additive functionals of McKean–Vlasov SDEs is characterized by PDEs on the product space [Formula: see text] equipped with the usual derivative in space variable and Lions’ derivative in distribution. These PDEs are solved by using probabilistic arguments developed from Ref. 2. As a consequence, the path independence of Girsanov transformations is identified with nonlinear PDEs on [Formula: see text] whose solutions are given by probabilistic arguments as well. In particular, the corresponding results on the Girsanov transformation killing the drift term derived earlier for the classical SDEs are recovered as special situations.

scholarly journals Simulation of anyonic statistics and its topological path independence using a seven-qubit quantum simulator

2016 ◽  
Vol 18 (4) ◽  
pp. 043043 ◽  
Author(s):  
Annie Jihyun Park ◽  
Emma McKay ◽  
Dawei Lu ◽  
Raymond Laflamme
Keyword(s):  
Path Independence ◽  
Quantum Simulator

Approximations of boundary crossing probabilities for a Brownian motion

1999 ◽  
Vol 36 (4) ◽  
pp. 1019-1030 ◽  
Author(s):  
Alex Novikov ◽  
Volf Frishling ◽  
Nino Kordzakhia
Keyword(s):  
Brownian Motion ◽  
Power Series ◽  
Numerical Integration ◽  
Piecewise Linear ◽  
Boundary Crossing ◽  
Square Root ◽  
Girsanov Transformation ◽  
Piecewise Linear Approximations ◽  
Infinite Power ◽  
Crossing Probabilities

Using the Girsanov transformation we derive estimates for the accuracy of piecewise approximations for one-sided and two-sided boundary crossing probabilities. We demonstrate that piecewise linear approximations can be calculated using repeated numerical integration. As an illustrative example we consider the case of one-sided and two-sided square-root boundaries for which we also present analytical representations in a form of infinite power series.

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