Fetching the paper…
Reading the bibliography…
We study semi-linear elliptic PDEs with polynomial non-linearity and provide a probabilistic representation of their solution using branching diffusion processes.
The extinction conditions for branching processes with diffusion
B. A. Sevast ′ janov · 1961
Earlier work this paper cites.
Partial differential equations of parabolic type
A. Friedman · 1964
Earlier work this paper cites.
Branching diffusion processes
A. V. Skorohod · 1964
Earlier work this paper cites.
On the branching process for Brownian particles with an absorbing boundary
S. Watanabe · 1965
Earlier work this paper cites.
Linear and quasilinear equations of parabolic type
O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural ′ ceva · 1968
Earlier work this paper cites.
Quasi-stationary behaviour of a left-continuous random walk
D. J. Daley · 1969
Earlier work this paper cites.
Branching Markov processes. III
N. Ikeda, M. Nagasawa, and S. Watanabe · 1969
Earlier work this paper cites.
Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov
H. P. McKean · 1975
Earlier work this paper cites.
On the existence of positive solutions of semilinear elliptic equations
P. L. Lions · 1982
Earlier work this paper cites.
Functional integration and partial differential equations , volume 109 of Annals of Mathematics Studies
M. Freidlin · 1985
Earlier work this paper cites.
Adapted solution of a backward stochastic differential equation
É. Pardoux and S. G. Peng · 1990
Earlier work this paper cites.
Simulation du mouvement brownien et des diffusions
O. Faure · 1992
Earlier work this paper cites.
Positive harmonic functions and diffusion , volume 45 of Cambridge Studies in Advanced Mathematics
R. G. Pinsky · 1995
Cited alongside, same era.
Backwards sde with random terminal time and applications to semilinear elliptic pde
R. W. R. Darling and E. Pardoux · 1997
Cited alongside, same era.
On the differentiation of heat semigroups and Poisson integrals
A. Thalmaier · 1997
Cited alongside, same era.
Diffusions and elliptic operators
R. F. Bass · 1998
Cited alongside, same era.
Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order
É. Pardoux · 1998
Cited alongside, same era.
Simulation of a space-time bounded diffusion
G. N. Milstein and M. V. Tretyakov · 1999
A regression-based Monte Carlo method to solve backward stochastic differential equations
E. Gobet, J.-P. Lemor, and X. Warin · 2005
Later among the works it cites.
Strong approximations of bsdes in a domain
B. Bouchard and S. Menozzi · 2009
Later among the works it cites.
Monte carlo solution of cauchy problem for a nonlinear parabolic equation
A. Rasulov, G. Raimova, and M. Mascagni · 2010
Later among the works it cites.
Semilinear elliptic equations for beginners
M. Badiale and E. Serra · 2011
Later among the works it cites.
exitbm: a library for simulating Brownian motion’s exit times and positions from simple domains
A. Lejay · 2011
Later among the works it cites.
Branching processes , volume 196
K. B. Athreya and P. E. Ney · 2012
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
BSDEs, weak convergence and homogenization of semilinear PDEs , pages 503–549
É. Pardoux · 1999
Cited alongside, same era.
Lp solutions of backward stochastic differential equations
P. Briand, B. Delyon, Y. Hu, E. Pardoux, and L. Stoica · 2003
Cited alongside, same era.
Estimates of the solutions of a system of quasi-linear PDEs. A probabilistic scheme
F. Delarue · 2003
Cited alongside, same era.
Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
B. Bouchard and N. Touzi · 2004
Cited alongside, same era.
Revisiting the Greeks for European and American options
E. Gobet · 2004
Cited alongside, same era.
J. Zhang · 2004
Cited alongside, same era.
First time to exit of a continuous Itô process: General moment estimates and L1-convergence rate for discrete time approximations
B. Bouchard, S. Geiss, and E. Gobet · 2013
Later among the works it cites.
A numerical algorithm for a class of BSDEs via the branching process
P. Henry-Labordere, X. Tan, and N. Touzi · 2014
Later among the works it cites.
Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation
M. Bossy, N. Champagnat, H. Leman, S. Maire, L. Violeau, and M. Yvinec · 2015
Later among the works it cites.
Elliptic partial differential equations of second order
D. Gilbarg and N. S. Trudinger · 2015
Later among the works it cites.
Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
P. Henry-Labordere, N. Oudjane, X. Tan, N. Touzi, and X. Warin · 2016
Later among the works it cites.