On the Unique Solvability of Some Nonlinear Stochastic Pdes
نویسنده
چکیده
The Cauchy problem for 1-dimensional nonlinear stochastic partial differential equations is studied. The uniqueness and existence of solutions in Hp(T )-space are proved. 1991 Mathematics Subject Classification. 60H15, 35R60.
منابع مشابه
Uniqueness of L solutions for multidimensional BSDEs and for systems of degenerate parabolic PDEs with superlinear growth generator
We deal with the unique solvability of multidimensional backward stochastic differential equations (BSDEs) with a p-integrable terminal condition (p > 1) and a superlinear growth generator. We introduce a new local condition, on the generator (see Assumption (H4)), then we show that it ensures the existence and uniqueness, as well as the L-stability of solutions. Since the generator is of super...
متن کاملA note on unique solvability of the absolute value equation
It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...
متن کاملNumerical solvability of system of Fredholm-Hammerstein integral equations using Modification of Hat Function
A system of integral equations can describe different kind of problems in sciences and engineering. There are many different methods for numerical solution of linear and nonlinear system of integral equations. This paper proposed a numerical method based on modification of Hat functions for solving system of Fredholm-Hammerstein integral equations. The proposed method reduced a system of integr...
متن کامل2 on the Solvability of Nonlinear Spdes
The Cauchy problem for 1-dimensional nonlinear sto-chastic partial diierential equations is studied. The uniqueness and existence of solutions in H 2 p (T)-space are proved. 1. Introduction The aim of this paper is to prove the unique solvability of the following one-dimensional nonlinear stochastic partial diierential equa-tions(SPDEs): du = a(t; x; u)u 00 + f(t; x)] dt + k (t)u 0 + g k (t; x)...
متن کاملContinuous Dependence Estimates for Viscosity Solutions of Integro-pdes
We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs. We use this framework to provide explicit estimates for the continuous dependence on the coefficients and the “Lévy measure” in the Bellman/Isaacs integro-PDEs arising in stochastic control/differential games. M...
متن کامل