Existence Results for Some Partial Stochastic Differential Equations

2011 ◽  
pp. 143-195
Author(s):  
Paul H. Bezandry ◽  
Toka Diagana
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence Results

scholarly journals Some Existence Results for Systems of Impulsive Stochastic Differential Equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sliman Mekki ◽  
Tayeb Blouhi ◽  
Juan J. Nieto ◽  
Abdelghani Ouahab
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Impulsive Systems ◽  
Uniqueness Of Solutions

Abstract In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.

scholarly journals Quantum stochastic operator cocycles via associated semigroups

2007 ◽  
Vol 142 (3) ◽  
pp. 535-556 ◽  
Author(s):  
J. MARTIN LINDSAY ◽  
STEPHEN J. WILLS
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
General Principle ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Necessary And Sufficient Conditions ◽  
Contraction Operator ◽  
Stochastic Operator ◽  
Necessary And Sufficient

AbstractA recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their stochastic generators. This leads to new existence results for quantum stochastic differential equations. We also give necessary and sufficient conditions for a cocycle to satisfy such an equation.

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law
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