scholarly journals Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation

2017 ◽  
Vol 127 (2) ◽  
pp. 359-384 ◽  
Author(s):  
Seiichiro Kusuoka
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Density Functions ◽  
Path Dependent

Stochastic formulations of the parametrix method

2018 ◽  
Vol 22 ◽  
pp. 178-209
Author(s):  
Arturo Kohatsu-Higa ◽  
Gô Yûki
Keyword(s):  
Differential Equations ◽  
Fixed Points ◽  
Stochastic Differential Equations ◽  
Probability Density ◽  
Lower Bounds ◽  
Probability Density Functions ◽  
Upper And Lower Bounds ◽  
Density Functions ◽  
Holder Continuity ◽  
Gaussian Type

In this manuscript, we consider stochastic expressions of the parametrix method for solutions of d-dimensional stochastic differential equations (SDEs) with drift coefficients which belong to Lp(Rd), p > d. We prove the existence and Hölder continuity of probability density functions for distributions of solutions at fixed points and obtain an explicit expansion via (stochastic) parametrix methods. We also obtain Gaussian type upper and lower bounds for these probability density functions.

scholarly journals The dual Yamada–Watanabe theorem for mild solutions to stochastic partial differential equations

2021 ◽  
Vol 105 (0) ◽  
pp. 51-68
Author(s):  
S. Tappe
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Mild Solutions ◽  
Moving Frame ◽  
Partial Differential ◽  
Infinite Dimensional ◽  
Dual Result ◽  
Path Dependent

We provide the dual result of the Yamada–Watanabe theorem for mild solutions to semilinear stochastic partial differential equations with path-dependent coefficients. An essential tool is the so-called “method of the moving frame”, which allows us to reduce the proof to infinite dimensional stochastic differential equations.

Path-dependent BSDEs with jumps and their connection to PPIDEs

2016 ◽  
Vol 17 (05) ◽  
pp. 1750036 ◽  
Author(s):  
Eduard Kromer ◽  
Ludger Overbeck ◽  
Jasmin A. L. Röder
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Viscosity Solution ◽  
Path Dependence ◽  
Backward Stochastic Differential Equations ◽  
Terminal Condition ◽  
Path Dependent

We study path-dependent backward stochastic differential equations (BSDEs) with jumps. In this context path-dependence of a BSDE is the dependence of the BSDE-terminal condition and the BSDE-generator of a path of a càdlàg process. We study the path-differentiability of BSDEs of this type and establish a connection to path-dependent PIDEs in terms of the existence of a viscosity solution and the respective Feynman–Kac theorem.

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law
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