Research output: Contribution to journal › Article
A Stochastic Interpretation of the Cauchy Problem Solution for the Equation ∂u/∂t=(σ^2/2)Δu+V(x)u with Complex σ. / Faddeev, M.M.; Ibragimov, I.A.; Smorodina, N.V.
In: Markov Processes and Related Fields, Vol. 22, No. 2, 2016, p. 203-226.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A Stochastic Interpretation of the Cauchy Problem Solution for the Equation ∂u/∂t=(σ^2/2)Δu+V(x)u with Complex σ.
AU - Faddeev, M.M.
AU - Ibragimov, I.A.
AU - Smorodina, N.V.
PY - 2016
Y1 - 2016
N2 - Using classical probabilistic methods we construct a probabilistic approximation in $L_2$ of the Cauchy problem solution for an equation $\frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\,\Delta u+V(x)u,$ where $\mathrm{Re}\,V\leqslant 0$ and $\sigma$ is a complex parameter with $\mathrm{Re}\,\sigma^2\geqslant 0$. This equation coincides with the heat equation when $\mathrm{Im}\,\sigma=0$ and with the Schr\"odinger equation when $\mathrm{Re}\,\sigma^2=0$.
AB - Using classical probabilistic methods we construct a probabilistic approximation in $L_2$ of the Cauchy problem solution for an equation $\frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\,\Delta u+V(x)u,$ where $\mathrm{Re}\,V\leqslant 0$ and $\sigma$ is a complex parameter with $\mathrm{Re}\,\sigma^2\geqslant 0$. This equation coincides with the heat equation when $\mathrm{Im}\,\sigma=0$ and with the Schr\"odinger equation when $\mathrm{Re}\,\sigma^2=0$.
KW - Limit theorem
KW - Schr\"odinger equation
KW - Feynman measure
KW - random walk
KW - evolution equation
M3 - Article
VL - 22
SP - 203
EP - 226
JO - Markov Processes and Related Fields
JF - Markov Processes and Related Fields
SN - 1024-2953
IS - 2
ER -
ID: 7587928