Journal Article10.1070/SM1981V039N03ABEH001522
On strong solutions and explicit formulas for solutions of stochastic integral equations
TL;DR: In this article, conditions are obtained under which the stochastic equation has a strong solution in the multidimensional case where the diffusion matrix is the identity matrix and the drift vector is bounded.
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Abstract: Conditions are obtained under which the stochastic equation has a strong solution. In particular, in the multidimensional case where the diffusion matrix is the identity matrix and the drift vector is bounded, these conditions are satisfied. Bibliography: 13 titles.
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Citations
Zero-Sum Risk-Sensitive Stochastic Differential Games
Arnab Basu,Mrinal K. Ghosh +1 more
TL;DR: The value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups of the Hamilton--Jacobi--Isaacs equations.
31
The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions
TL;DR: In this paper, the authors examined the solution properties of the Burgers' equation with stochastic transport and proved the local existence and uniqueness of smooth solutions in the inviscid case and constructed a blow-up criterion.
On the Smoothness of Value Functions and the Existence of Optimal Strategies
TL;DR: In this article, the authors prove that the value function for the optimal control of any time-homogeneous, one-dimensional di usion is twice continuously di erentiable, under Lipschitz, growth, and non-vanishing volatility conditions.
The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate
TL;DR: In this paper, the long time properties of the Euler scheme applied to SDEs with a piecewise constant drift and a constant diffusion coefficient were analyzed, and a rank-based stock market model describing the evolution of the capital distribution within the market was provided.
•Posted Content
Finite state mean field games with Wright Fisher common noise as limits of N-player weighted games
TL;DR: In this paper, it was shown that the finite player version of the game can converge to the solution of a Wright-Fisher mean field game with common noise in the presence of finite players.
29
References
•Book
Linear and Quasilinear Equations of Parabolic Type
Olga Aleksandrovna Ladyzhenskaia
- 31 Dec 1969
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
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A transformation of the phase space of a diffusion process that removes the drift
TL;DR: In this paper, a quasi-isometric transformation of a phase space that allows passing from a diffusion process with nonzero drift coefficient to a process without drift is presented, and strong solutions of stochastic differential equations with a "bad" drift coefficient are constructed.
543
On explicit formulas for solutions of stochastic equations
TL;DR: In this paper, the authors prove the existence of a strong solution of a stochastic integral equation of the form, using the theory of differential equations of parabolic type, and prove the proof of these criteria is based on finding formulas expressing via multiple Stochastic integrals, formulas which in the case give an expression for, if is a strong solutions of the stochastically equation.
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