Solving linear parabolic rough partial differential equations
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Summary
This work proposes a regression Monte Carlo algorithm for spatio-temporal approximation of the solution of a linear parabolic partial differential equation driven by a deterministic rough path of Holder regularity with 1/3 < α ≤ 1/2.
- Type
- preprint
- Published
- 2018-03-26
- Cited by
- 5
- References
- 34
- Access
- Open access
- OpenAlex
- https://openalex.org/W2794846593
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:119579782
Keywords
Mathematics, Partial differential equation, Parabolic partial differential equation, Stochastic partial differential equation, Elliptic partial differential equation
References
- Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
- An introduction to the geometry of stochastic flows
- Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations
- Multidimensional Stochastic Processes as Rough Paths: Theory and Applications
- A Distribution-Free Theory of Nonparametric Regression
- Ordinary Differential Equations
- Rough paths, Signatures and the modelling of functions on streams
- Stochastic Numerics for Mathematical Physics
- Non-standard approximations of the Ito-map
- Stochastic partial differential equations: a rough path view
- The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations
- A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations
- Di erential equations driven by rough signals
- Solving the Dirichlet problem for Navier–Stokes equations by probabilistic approach
- Abstract nonlinear filtering theory in the presence of fractional Brownian motion
- Integrability of (Non-)Linear Rough Differential Equations and Integrals
- A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion
- A (rough) pathwise approach to a class of non-linear stochastic partial differential equations
- Integrability Estimates for Gaussian Rough Differential Equations
- Solving the KPZ equation
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