TY - JOUR
T1 - Brownian trajectory is a regular lateral boundary for the heat equation
AU - Krylov, Nicolai V
PY - 2003/11/20
Y1 - 2003/11/20
N2 - The one-dimensional heat equation in the domain x > wt, t > 0, is considered. Here wt is a trajectory of Brownian motion. For almost any trajectory, it is proved that if the boundary data are continuous, then the solution is continuous in the closure of the domain. The proof is based on Davis's law of square root for Brownian motion or on its weaker version, which is obtained by using the theory of stochastic partial differential equations.
AB - The one-dimensional heat equation in the domain x > wt, t > 0, is considered. Here wt is a trajectory of Brownian motion. For almost any trajectory, it is proved that if the boundary data are continuous, then the solution is continuous in the closure of the domain. The proof is based on Davis's law of square root for Brownian motion or on its weaker version, which is obtained by using the theory of stochastic partial differential equations.
KW - Fine properties of Brownian motion
KW - Heat equation in irregular cylinders
KW - Stochastic partial differential equations
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U2 - 10.1137/S0036141002402980
DO - 10.1137/S0036141002402980
M3 - Article
AN - SCOPUS:0242596346
SN - 0036-1410
VL - 34
SP - 1167
EP - 1182
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 5
ER -