On the existence of solutions of stochastic differential equations with singular drifts

1987 ◽  
Vol 74 (2) ◽  
pp. 295-315 ◽  
Author(s):  
Satoshi Takanobu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence Of Solutions

scholarly journals Comparison Theorems for the Multidimensional BDSDEs and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Bo Zhu ◽  
Baoyan Han
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Existence Of Solutions ◽  
Minimal Solution ◽  
Comparison Theorems ◽  
Doubly Stochastic

A class of backward doubly stochastic differential equations (BDSDEs) are studied. We obtain a comparison theorem of these multidimensional BDSDEs. As its applications, we derive the existence of solutions for this multidimensional BDSDEs with continuous coefficients. We can also prove that this solution is the minimal solution of the BDSDE.

Existence of Solutions for Stochastic Differential Equations under G-Brownian Motion with Discontinuous Coefficients

2012 ◽  
Vol 67 (12) ◽  
pp. 692-698 ◽  
Author(s):  
Faiz Faizullah
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence Of Solutions ◽  
Upper And Lower Solutions ◽  
Discontinuous Coefficients ◽  
Existence Theory ◽  
Discontinuous Functions ◽  
Vector Valued

The existence theory for the vector valued stochastic differential equations under G-Brownian motion (G-SDEs) of the type Xt = X0+ ∫to(v;Xv)dv+ ∫t0 g(v;Xv)d(B)v+ ∫t0 h(v;Xv)dBv; t ∊ [0;T]; with first two discontinuous coefficients is established. It is shown that the G-SDEs have more than one solution if the coefficient g or the coefficients f and g simultaneously, are discontinuous functions. The upper and lower solutions method is used and examples are given to explain the theory and its importance.

scholarly journals On the existence of solutions for stochastic differential equations driven by fractional Brownian motion

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1695-1700
Author(s):  
Zhi Li
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Growth Condition ◽  
Linear Growth ◽  
Existence Of Solutions ◽  
Hurst Parameter ◽  
Linear Growth Condition ◽  
Discontinuous Drift

In this paper, we are concerned with a class of stochastic differential equations driven by fractional Brownian motion with Hurst parameter 1/2 < H < 1, and a discontinuous drift. By approximation arguments and a comparison theorem, we prove the existence of solutions to this kind of equations under the linear growth condition.

Sign in / Sign up

Export Citation Format

Share Document